Graph Parabolas in Vertex Form
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Question 1 of 5
1. Question
Graph `y=(x+1)^2-5`.Hint
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Fantastic!
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The Basic Form of a Parabola
$$y=a(x- \color{blue}{h})^2+\color{blue}{k}$$$$\text{Vertex:} (\color{blue}{h},\color {blue}{k})$$Identify the vertex of the graph from the given formula.`y` `=` $$a(x-\color{blue}{h})^2+\color{blue}{k}$$ `y` `=` `(x+1)^2-5` Given equation `y` `=` $$a(x-(\color{blue}{-1}))^2+(\color{blue}{-5})$$ Extract values of `h` and `k` Vertex `=` $$(\color{blue}{h},\color{blue}{k})$$ Vertex `=` $$(\color{blue}{-1},\color{blue}{-5})$$ Mark the vertex on the graph.
Next, solve for the `y`-intercept by substituting `x=0`.`y` `=` `(x+1)^2-5` `y` `=` `(0+1)^2-5` Substitute `x=0` `y` `=` `1-5` `y` `=` `-4` Mark the `y`-intercept on the graph.
Draw a parabola using the points.
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Question 2 of 5
2. Question
Graph `y=-(x-1)^2+2`.Hint
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Excellent!
Incorrect
The Basic Form of a Parabola
$$y=a(x- \color{blue}{h})^2+\color{blue}{k}$$$$\text{Vertex:} (\color{blue}{h},\color {blue}{k})$$Identify the vertex of the graph from the given formula.`y` `=` $$a(x-\color{blue}{h})^2+\color{blue}{k}$$ `y` `=` `-(x-1)^2+2` Given equation `y` `=` $$(-1)(x-(\color{blue}{1}))^2+(\color{blue}{2})$$ Extract values of `h` and `k` Vertex `=` $$(\color{blue}{h},\color{blue}{k})$$ Vertex `=` $$(\color{blue}{1},\color{blue}{2})$$ Mark the vertex on the graph.
Next, solve for the `y`-intercept by substituting `x=0`.`y` `=` `-(x-1)^2+2` `y` `=` `-(0-1)^2+2` Substitute `x=0` `y` `=` `-1+2` `y` `=` `1` Mark the `y`-intercept on the graph.
Draw a parabola using the points.
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Question 3 of 5
3. Question
Graph `y=-(x+1)^2-2`.Hint
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Nice Job!
Incorrect
The Basic Form of a Parabola
$$y=a(x- \color{blue}{h})^2+\color{blue}{k}$$$$\text{Vertex:} (\color{blue}{h},\color {blue}{k})$$Identify the vertex of the graph from the given formula.`y` `=` $$a(x-\color{blue}{h})^2+\color{blue}{k}$$ `y` `=` `-(x+1)^2-2` Given equation `y` `=` $$(-1)(x+(\color{blue}{1}))^2-(\color{blue}{2})$$ Extract values of `h` and `k` Vertex `=` $$(\color{blue}{h},\color{blue}{k})$$ Vertex `=` $$(\color{blue}{-1},\color{blue}{-2})$$ Mark the vertex on the graph.
Next, solve for the `y`-intercept by substituting `x=0`.`y` `=` `-(x+1)^2-2` `y` `=` `-(0+1)^2-2` Substitute `x=0` `y` `=` `-1-2` `y` `=` `-3` Mark the `y`-intercept on the graph.
Draw a parabola using the points.
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Question 4 of 5
4. Question
Graph `y=-(x-4)^2+5`.Hint
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Well Done!
Incorrect
The Basic Form of a Parabola
$$y=a(x- \color{blue}{h})^2+\color{blue}{k}$$$$\text{Vertex:} (\color{blue}{h},\color {blue}{k})$$Identify the vertex of the graph from the given formula.`y` `=` $$a(x-\color{blue}{h})^2+\color{blue}{k}$$ `y` `=` `-(x-4)^2+5` Given equation `y` `=` $$(-1)(x-(\color{blue}{4}))^2+(\color{blue}{5})$$ Extract values of `h` and `k` Vertex `=` $$(\color{blue}{h},\color{blue}{k})$$ Vertex `=` $$(\color{blue}{4},\color{blue}{5})$$ Mark the vertex on the graph.
Next, solve for the `y`-intercept by substituting `x=0`.`y` `=` `-(x-4)^2+5` `y` `=` `-(0-4)^2+5` Substitute `x=0` `y` `=` `-16+5` `y` `=` `-11` Mark the `y`-intercept on the graph.
Draw a parabola using the points.
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Question 5 of 5
5. Question
Graph `y=(x-3)^2+2`.Hint
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Exceptional!
Incorrect
The Basic Form of a Parabola
$$y=a(x- \color{blue}{h})^2+\color{blue}{k}$$$$\text{Vertex:} (\color{blue}{h},\color {blue}{k})$$Identify the vertex of the graph from the given formula.`y` `=` $$a(x-\color{blue}{h})^2+\color{blue}{k}$$ `y` `=` `(x-3)^2+2` Given equation `y` `=` $$(x-(\color{blue}{3}))^2+(\color{blue}{2})$$ Extract values of `h` and `k` Vertex `=` $$(\color{blue}{h},\color{blue}{k})$$ Vertex `=` $$(\color{blue}{3},\color{blue}{2})$$ Mark the vertex on the graph.
Next, solve for the `y`-intercept by substituting `x=0`.`y` `=` `(x-3)^2+2` `y` `=` `(0-3)^2+2` Substitute `x=0` `y` `=` `9+2` `y` `=` `11` Mark the `y`-intercept on the graph.
Draw a parabola using the points.
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