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Question 1 of 5
Which of the following shows the graph of y=x2+3y=x2+3?
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First, identify the vertex of the parabola from the equation.
yy |
== |
aax2+x2+CC |
yy |
== |
((11)x2+)x2+33 |
Highlight values of aa and CC |
aa |
== |
11 |
CC |
== |
33 |
Vertex is at (0,(0,CC)), so the graph’s vertex is at (0,(0,33)).
Plot the vertex on the graph.
Because the value of aa is positive, the parabola is concave up. Draw a parabola from the vertex.
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Question 2 of 5
Which of the following shows the graph of y=x2y=x2?
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First, identify the vertex of the parabola from the equation.
yy |
== |
aax2+x2+CC |
yy |
== |
x2x2 |
yy |
== |
((11)x2+)x2+00 |
Highlight values of aa and CC |
aa |
== |
11 |
CC |
== |
00 |
Vertex is at (0,(0,CC)), so the graph’s vertex is at (0,(0,00)).
Plot the vertex on the graph.
Because the value of aa is positive, the parabola is concave up. Draw a parabola from the vertex.
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Question 3 of 5
Which of the following shows the graph of y=x2-4y=x2−4?
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First, identify the vertex of the parabola from the equation.
yy |
== |
aax2+x2+CC |
yy |
== |
x2x2 |
yy |
== |
((11)x2+()x2+(-4−4)) |
Highlight values of aa and CC |
aa |
== |
11 |
CC |
== |
-4−4 |
Vertex is at (0,(0,CC)), so the graph’s vertex is at (0,(0,-4−4)).
Plot the vertex on the graph.
Because the value of aa is positive, the parabola is concave up. 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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If a>0a>0, the parabola is concave up.
If a<0a<0, the parabola is concave down.
A big aa means a narrow parabola while a small aa means it is wide.
A point on the parabola is ((22,2020)).Substitute the values of xx and yy into the equation for parabola.
yy |
== |
ax2ax2 |
Equation of the parabola |
2020 |
== |
a(2)2a(2)2 |
x=2x=2 and y=20y=20 |
2020 |
== |
4a4a |
Simplify |
55 |
== |
aa |
Divide both sides by 44 |
aa |
== |
55 |
Substitute the value of aa back to the equation.
yy |
== |
ax2ax2 |
Equation of the parabola |
yy |
== |
5x25x2 |
a=5a=5 |
yy |
== |
5x25x2 |
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Question 5 of 5
Which of the following shows the equation of the graph below?
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If a>0a>0, the parabola is concave up.
If a<0a<0, the parabola is concave down.
A big aa means a narrow parabola while a small aa means it is wide.
A point on the parabola is ((-3−3,-3−3)).Substitute the values of xx and y into the equation for parabola.
y |
= |
ax2 |
Equation of the parabola |
-3 |
= |
a(−3)2 |
x=-3 and y=-3 |
-3 |
= |
9a |
Simplify |
-13 |
= |
a |
Divide both sides by 9 |
|
a |
= |
-13 |
Substitute the value of a back to the equation.
y |
= |
ax2 |
Equation of the parabola |
y |
= |
−13x2 |
a=-13 |
|
y |
= |
-13x2 |