LT 4.3 I can translate quadratic equations from factored and vertex forms INTO standard form.
4.3 Practice C: Convert Vertex Form to Standard Form
Write in Standard Form
1. y = (x – 3)2 + 1
3.
y = -(x + 4)2 – 8
5. y = -2(x + 7)2 – 10
2. y = -2(x – 3)2 – 6
4. y = (x – 8)2 + 3
6. y =2.4(x – 5.1)2 + 3
Determine whether the equations in each pair are equivalent.
7. y = 2(x – 3)2 – 7
y = 2x2 – 12x + 11
8. y = 2(x + 4)2 + 8
y = 2x2 – 16x + 32
For 9-12, find the vertex, convert to standard form, find the y-intercept and graph.
9. y = (x – 1)2 – 16
a. vertex:
10. y = 2(x +3)2 + 7
a. vertex:
b. Standard Form:
b. Standard Form:
c. y-intercept:
c. y-intercept:
d. Make a table and graph
d. Make a table and graph
4.3 Practice C
P - 102
LT 4.3 I can translate quadratic equations from factored and vertex forms INTO standard form.
Match each equation with the correct statement.
11. y = x2 + 5x + 3
a. The vertex is at (2, 3).
12. y = (x – 2)2 + 3
b. The y-intercept is 5.
13. y = 2(x – 5)2 + 3
c. The y-intercept is 3.
14. y = x2 + 3x + 5
d. The vertex is at (5, 3).
15. Which of the following represent the same parabola as y = 2(x – 3)2 – 2?
a. y = -(x – 2)(x – 4)
b. y = 3(x – 4)(x + 2)
c. y = 2(x – 4)(x – 2)
d. y = 2(x – 3)(x + 1)
Expand each equation to standard form. Use a graphing calculator to check your answer. Graph each
equation: Enter the original equation as Y1 and the standard form equation as Y2). If you expanded the
equation correctly, the second parabola should be graphed on top of the first equation. If you see two
parabolas…go back and check your work.
13. y = -(x – 6)2 + 2
14. y = 2(x + 1)2 – 4
a. Standard Form:
a. Standard Form:
b. Sketch the graph:
b. Sketch the graph:
4.3 Practice C
P - 103
LT 4.3 I can translate quadratic equations from factored and vertex forms INTO standard form.
15. The Galleria, in BCE Place in Toronto, has many beautiful parabolic arches. One of the arches
can be modeled by the function y = -0.5(x – 6.8)2 + 26. The x-axis represents the floor in the
Galleria and the y-axis represents the height above the floor. Distances are in meters.
a. Write the function in standard form.
b. What is the height of the arch at its center?
c. The y-intercept represents the lowest point at one side of the base of an arch. What is
this height?
16. The height, h, of a baseball thrown off a bridge can be modeled by the equation h = -5(t – 4)2 +
130 where the height is measured in meters and t is the time in seconds since the ball was
thrown.
a. How high was the ball thrown?
b. How long did the ball take to reach its highest point?
c. How high was the bridge
d. Make a table and graph.
4.3 Practice C
P - 104