Tutorial Exercise Write an equation for the parabola in standard form. y 10 (0, 7) - 10 -5 10 (-3, –2) -5 - 10f Step 1 First, determine the vertex from the graph. (х, у) %3D -3, – 2 -3, -2

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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Chapter7: Conic Sections And Quadratic Systems
Section7.CR: Chapter Review
Problem 17E
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Tutorial Exercise
Write an equation for the parabola in standard form.
y
10
(0, 7)
- 10
-5
10
(-3, –2)
-5
- 10f
Step 1
First, determine the vertex from the graph.
(х, у) %3D
-3, – 2
-3, -2
Transcribed Image Text:Tutorial Exercise Write an equation for the parabola in standard form. y 10 (0, 7) - 10 -5 10 (-3, –2) -5 - 10f Step 1 First, determine the vertex from the graph. (х, у) %3D -3, – 2 -3, -2
Step 2
A quadratic function in standard form is given by the following equation.
f(x) = a(x – h)² + k
The vertex (h, k) can be used to fill in the blanks below.
f(x) = a(x - (-3 v
|-2 V
+
f(x) =
x +
3
-
Step 3
Finally, determine a. The parabola passes through the point (0, 7). Substitute the values of x and y into the
equation.
= a
- 2
Solve for a. Simplify the coefficient of a and move all constant terms to the left side of the equation.
9 =
Simplify.
a =
Step 4
We can now write the equation in standard form. Use y in place of f(x).
Transcribed Image Text:Step 2 A quadratic function in standard form is given by the following equation. f(x) = a(x – h)² + k The vertex (h, k) can be used to fill in the blanks below. f(x) = a(x - (-3 v |-2 V + f(x) = x + 3 - Step 3 Finally, determine a. The parabola passes through the point (0, 7). Substitute the values of x and y into the equation. = a - 2 Solve for a. Simplify the coefficient of a and move all constant terms to the left side of the equation. 9 = Simplify. a = Step 4 We can now write the equation in standard form. Use y in place of f(x).
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