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Write the Equation of a Parabola from the Graph>
Write a Parabola from the GraphWrite a Parabola from the Graph
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Question 1 of 7
1. Question
Find the equation of the graph below
Hint
Help VideoCorrect
Great Work!
Incorrect
Intercept Form
`y=a(x-``p``)(x-``q``)`where `p` and `q` are the `x` interceptsSince the graph indicates the intercepts, use the Intercept Form. Slot the `x` and `y` intercepts into the Intercept Form to find `a`. Then, substitute `a` and the `x` intercepts to the main formula to form an equation.First, identify the `x` and `y` intercepts from the graphRemember that an intercept is where the graph touches the `x` or `y` axis
`p` `=` `1` `x`-intercept `q` `=` `4` `x`-intercept `y` `=` `4` `y`-intercept `x` `=` `0` Value of `x` at the `y`-intercept Now, slot these values into the Intercept Form and solve for `a``y` `=` `a(x-``p``)(x-``q``)` Intercept Form `4` `=` `a(0-``1``)(0-``4``)` Substitute values `4` `=` `a(-1)(-4)` `4` `=` `4a` `4``-:4` `=` `4a``-:4` `1` `=` `a` `a` `=` `1` Finally, substitute `a` and the `x` intercepts into the Intercept Form`y` `=` `a(x-``p``)(x-``q``)` Intercept Form `y` `=` `1(x-``1``)(x-``4``)` Substitute values `y` `=` `(x-1)(x-4)` `y=(x-1)(x-4)` -
Question 2 of 7
2. Question
Find the equation of the graph below
Hint
Help VideoCorrect
Well Done!
Incorrect
Intercept Form
`y=a(x-``p``)(x-``q``)`where `p` and `q` are the `x` interceptsSince the graph indicates the intercepts, use the Intercept Form. Slot the `x` and `y` intercepts into the Intercept Form to find `a`. Then, substitute `a` and the `x` intercepts to the main formula to form an equation.First, identify the `x` and `y` intercepts from the graphRemember that an intercept is where the graph touches the `x` or `y` axis
`p` `=` `-3` `x`-intercept `q` `=` `5` `x`-intercept `y` `=` `15` `y`-intercept `x` `=` `0` Value of `x` at the `y`-intercept Now, slot these values into the Intercept Form and solve for `a``y` `=` `a(x-``p``)(x-``q``)` Intercept Form `15` `=` `a(0-(``-3``))(0-``5``)` Substitute values `15` `=` `a(3)(-5)` `15` `=` `-15a` `15``-:(-15)` `=` `-15a``-:(-15)` `-1` `=` `a` `a` `=` `-1` Finally, substitute `a` and the `x` intercepts into the Intercept Form`y` `=` `a(x-``p``)(x-``q``)` Intercept Form `y` `=` `-1(x-(``-3``))(x-``5``)` Substitute values `y` `=` `-(x+3)(x-5)` `y=-(x+3)(x-5)` -
Question 3 of 7
3. Question
Find the equation of the parabola given the following information`x=-1`
`x=5`
Vertex: `(2,-9)`Hint
Help VideoCorrect
Excellent!
Incorrect
Equation of a Parabola
`y=a(x-``p``)(x-``q``)`First, draw a parabola from the two values of `x` and the vertex `(2,-9)`.
Substitute the values of `x` into the formula.`y` `=` `a(x-``p``)(x-``q``)` `=` `a(x-``(-1)``)(x-``5``)` `p=-1` and `q=5` `y` `=` `a(x+1)(x-5)` Simplify Substitute the vertex `(2,-9)` into the equation to solve for `a`.`y` `=` `a``(x+1)(x-5)` `-9` `=` `a``(``2``+1)(``2``-5)` `x=2` and `y=-9` `-9` `=` `a``(3)(-3)` Simplify `-9` `=` `-9``a` `1` `=` `a` Divide both sides by `-9` `a` `=` `1` Substitute the value of `a` into the formula.`y` `=` `a``(x+1)(x-5)` `y` `=` `1``(x+1)(x-5)` `a=1` `y` `=` `x^2-4x-5` Simplify the equation `y=x^2-4x-5` -
Question 4 of 7
4. Question
Find the equation of the parabola given the following information`x=-2`
`x=4`
Vertex: `(2,-8)`Hint
Help VideoCorrect
Nice Job!
Incorrect
Equation of a Parabola
`y=a(x-``p``)(x-``q``)`First, draw a parabola from the two values of `x` and the vertex `(2,-8)`.
Substitute the values of `x` into the formula.`y` `=` `a(x-``p``)(x-``q``)` `=` `a(x-``(-2)``)(x-``4``)` `p=-2` and `q=4` `y` `=` `a(x+2)(x-4)` Simplify Substitute the vertex `(2,-8)` into the equation to solve for `a`.`y` `=` `a``(x+2)(x-4)` `-8` `=` `a``(``2``+2)(``2``-4)` `x=2` and `y=-8` `-8` `=` `a``(4)(-2)` Simplify `-8` `=` `-8``a` `1` `=` `a` Divide both sides by `-8` `a` `=` `1` Substitute the value of `a` into the formula.`y` `=` `a``(x+2)(x-4)` `y` `=` `1``(x+2)(x-4)` `a=1` `y` `=` `x^2-2x-8` Simplify the equation `y=x^2-2x-8` -
Question 5 of 7
5. Question
Find the equation of the parabola given the following information`x=-2`
`x=3`
Vertex: `(2,8)`Hint
Help VideoCorrect
Well Done!
Incorrect
Equation of a Parabola
`y=a(x-``p``)(x-``q``)`First, draw a parabola from the two values of `x` and the vertex `(2,8)`.
Substitute the values of `x` into the formula.`y` `=` `a(x-``p``)(x-``q``)` `=` `a(x-``(-2)``)(x-``3``)` `p=-2` and `q=3` `y` `=` `a(x+2)(x-3)` Simplify Substitute the vertex `(2,8)` into the equation to solve for `a`.`y` `=` `a``(x+2)(x-3)` `8` `=` `a``(``2``+2)(``2``-3)` `x=2` and `y=8` `8` `=` `a``(4)(-1)` Simplify `8` `=` `-4``a` `-2` `=` `a` Divide both sides by `-4` `a` `=` `-2` Substitute the value of `a` into the formula.`y` `=` `a``(x+2)(x-3)` `y` `=` `-2``(x+2)(x-3)` `a=-2` `y` `=` `-2(x^2-x-6)` `y` `=` `-2x^2+2x+12` Simplify the equation `y=-2x^2+2x+12` -
Question 6 of 7
6. Question
Find the equation of the parabola if `(0,8)` and `(2,0)` are points on the line.
Hint
Help VideoCorrect
Great Work!
Incorrect
Equation of a Parabola
$$y=\color{#ff0090}{a}\color{green}{x}^{2}+\color{blue}{b}\color{green}{x}+c$$$$\color{green}{x}=-\frac{\color{blue}{b}}{2\color{#ff0090}{a}}$$First, solve for `b` using the value of the `x`-intercept.`x` `=` $$\frac{-\color{blue}{b}}{2\color{#ff0090}{a}}$$ `2` `=` $$\frac{-\color{blue}{b}}{2\color{#ff0090}{a}}$$ `x=2` `4``a` `=` `-b` Multiply both sides by `2a` `-4``a` `=` `b` Divide both sides by `-1` `b` `=` `-4``a` Substitute the values of `b` and `c` into the general formula.`y` `=` $$\color{#ff0090}{a}\color{green}{x}^{2}+\color{blue}{b}\color{green}{x}+c$$ `y` `=` $$\color{#ff0090}{a}\color{green}{x}^{2}+\color{blue}{-4a}\color{green}{x}+8$$ `b=-4a`,`c=8` Substitute the value of `x` and `y` into the resulting equation using the `x`-intercept of the graph to solve for `a`.`y` `=` $$\color{#ff0090}{a}\color{green}{x}^{2}+(-4\color{#ff0090}{a})\color{green}{x}+8$$ `0` `=` $$\color{#ff0090}{a}\color{green}{2}^{2}+(-4\color{#ff0090}{a})(\color{green}{2})+8$$ `x=2`,`y=0` `0` `=` `4``a``-8``a``+8` Simplify `0` `=` `-4``a``+8` `-8` `=` `-4``a` Subtract `8` from both sides `2` `=` `a` Divide both sides by `2` `a` `=` `2` Divide both sides by `2` Substitute the value of `a` into the equation for `b`.`b` `=` `-4``a` `b` `=` `-4``(2)` `a=2` `b` `=` `-8` Substitute the value of `a`,`b` and `c` into the general formula.`y` `=` `a``x^2+``b``x+c` `y` `=` `2``x^2+``(-8)``x+8` `a=2`,`b=-8`, `c=8` `y` `=` `2x^2-8x+8` `y` `=` `x^2-4x+4` Divide the expression by `2` `y` `=` `(x-2)^2` Express as a square of binomial `y=(x-2)^2` -
Question 7 of 7
7. Question
Find the equation of the parabola if `(1,8)` and `(0,6)` are points on the line.
Hint
Help VideoCorrect
Fantastic!
Incorrect
Equation of a Parabola
$$y=\color{#ff0090}{a}\color{green}{x}^{2}+\color{blue}{b}\color{green}{x}+c$$$$\color{green}{x}=-\frac{\color{blue}{b}}{2\color{#ff0090}{a}}$$First, solve for `b` using the value of the `x` in the point`(1,8)`.`x` `=` $$\frac{-\color{blue}{b}}{2\color{#ff0090}{a}}$$ `1` `=` $$\frac{-\color{blue}{b}}{2\color{#ff0090}{a}}$$ `x=1` `-2``a` `=` `b` Multiply both sides by `-2a` `b` `=` `-2``a` Substitute the values of `b` and `c` into the general formula.`y` `=` $$\color{#ff0090}{a}\color{green}{x}^{2}+\color{blue}{b}\color{green}{x}+c$$ `y` `=` $$\color{#ff0090}{a}\color{green}{x}^{2}+\color{blue}{-2a}\color{green}{x}+6$$ `b=-2a`,`c=6` Substitute the value of `x` and `y` into the resulting equation using the point `(1,8)` to solve for `a`.`y` `=` $$\color{#ff0090}{a}\color{green}{x}^{2}+(-2\color{#ff0090}{a})\color{green}{x}+6$$ `8` `=` $$\color{#ff0090}{a}\color{green}{1}^{2}+(-2\color{#ff0090}{a})(\color{green}{2})+6$$ `x=1`,`y=8` `8` `=` `a``-2``a``+6` Simplify `8` `=` `-a``+6` `2` `=` `-a` Subtract `6` from both sides `-2` `=` `a` Divide both sides by `-1` `a` `=` `-2` Divide both sides by `2` Substitute the value of `a` into the equation for `b`.`b` `=` `-2``a` `b` `=` `-2``(-2)` `a=-2` `b` `=` `4` Substitute the value of `a`,`b` and `c` into the general formula.`y` `=` `a``x^2+``b``x+c` `y` `=` `-2``x^2+``4``x+6` `a=-2`,`b=4`, `c=6` `y` `=` `-2x^2+4x+6` `y` `=` `-2(x^2-2x-3)` Factor out `2` Since the equation is in standard form `(``a``x^2+``b``x+``c``=0)` we can factorise using the cross method.`x^2` `-2``x` `-3``=0`To factorise, we need to find two numbers that add to `-2` and multiply to `-3``-3` and `1` fit both conditions`-3 + 1` `=` `-2` `-3 xx 1` `=` `-3` 
Read across to get the factors.`(x-3)(x+1)``y=-2(x-3)(x+1)`
Quizzes
- Intro to Parabolas 1
- Intro to Parabolas 2
- Intro to Parabolas 3
- Graphing Parabolas Using a Table of Values
- Graph Parabolas in Standard Form 1
- Graph Parabolas in Standard Form 2
- Graph Parabolas by Completing the Square
- Graph Parabolas in Vertex Form
- Write a Parabola from the Graph
- Write a Parabola Given the Vertex and Another Point