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Question 1 of 5
Which of the following shows the graph of y=-x2+5?
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First, identify the vertex of the parabola from the equation.
y |
= |
ax2+C |
y |
= |
-x2+5 |
y |
= |
(-1)x2+5 |
Highlight values of a and C |
a |
= |
-1 |
C |
= |
5 |
Vertex is at (0,C), so the graph’s vertex is at (0,5).
Plot the vertex on the graph.
Because the value of a is negative, the parabola is concave down. Draw a parabola from the vertex.
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Question 2 of 5
Which of the following shows the graph of y=-x2?
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First, identify the vertex of the parabola from the equation.
y |
= |
ax2+C |
y |
= |
-x2 |
y |
= |
(-1)x2+0 |
Highlight values of a and C |
a |
= |
-1 |
C |
= |
0 |
Vertex is at (0,C), so the graph’s vertex is at (0,0).
Plot the vertex on the graph.
Because the value of a is negative, the parabola is concave down. Draw a parabola from the vertex.
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Question 3 of 5
Which of the following shows the graph of y=-x2-2?
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First, identify the vertex of the parabola from the equation.
y |
= |
ax2+C |
y |
= |
-x2-2 |
y |
= |
(-1)x2+(-2) |
Highlight values of a and C |
a |
= |
-1 |
C |
= |
-2 |
Vertex is at (0,C), so the graph’s vertex is at (0,-2).
Plot the vertex on the graph.
Because the value of a is negative, the parabola is concave down. Draw a parabola from the vertex.
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Question 4 of 5
Which of the following shows the equation of the graph below?
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Solve for C using the y-intercept of the graph. The y-intercept is (0,-3).
y |
= |
ax2+C |
Equation of the parabola |
-3 |
= |
a(0)2+C |
x=0 and y=-3 |
-3 |
= |
C |
Simplify |
C |
= |
-3 |
A point on the parabola is (2,5).Substitute the values of x and y into the equation for parabola together with the value of C to solve for a.
y |
= |
ax2+C |
Equation of the parabola |
5 |
= |
a(2)2+(−3) |
x=2, y=5 and C=-3 |
5 |
= |
4a-3 |
Simplify |
8 |
= |
4a |
Add 3 to both sides |
2 |
= |
a |
Divide both sides by 4 |
a |
= |
2 |
Substitute the value of a back to the equation.
y |
= |
ax2+C |
Equation of the parabola |
y |
= |
2x2−3 |
a=2 and C=-3 |
y |
= |
2x2-3 |
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Question 5 of 5
Which of the following shows the equation of the graph below?
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Solve for C using the y-intercept of the graph. The y-intercept is (0,-1).
y |
= |
ax2+C |
Equation of the parabola |
-1 |
= |
a(0)2+C |
x=0 and y=-1 |
-1 |
= |
C |
Simplify |
C |
= |
-1 |
A point on the parabola is (-2,-3).Substitute the values of x and y into the equation for parabola together with the value of C to solve for a.
y |
= |
ax2+C |
Equation of the parabola |
-3 |
= |
a(−2)2+(−1) |
x=2, y=5 and C=-3 |
-3 |
= |
4a-1 |
Simplify |
-2 |
= |
4a |
Add 1 to both sides |
-12 |
= |
a |
Divide both sides by 4 |
a |
= |
-12 |
Substitute the value of a back to the equation.
y |
= |
ax2+C |
Equation of the parabola |
y |
= |
−12x2−1 |
a=-12 and C=-1 |
|
y |
= |
-12x2-1 |