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Back to Exercise: Use factoring and completing the square

Exercises: Use Factoring and Completing the Square

Work through each section in order. Show your work where indicated. For completing the square, show each step of the process.

Grade 9·19 problems·~30 min·Common Core Math - HS Functions·standard·hsf-if-c-8a
Work through problems with immediate feedback
A

Recall / Warm-Up

1

Which factored form is correct for f(x)=x2−7x+12f(x) = x^2 - 7x + 12?

2

What is the vertex of f(x)=(x−5)2+3f(x) = (x - 5)^2 + 3?

3

For the parabola f(x)=−2(x−1)2+7f(x) = -2(x - 1)^2 + 7, does the vertex represent a maximum or minimum value?

B

Fluency Practice

1

Factor f(x)=x2+x−12f(x) = x^2 + x - 12 and identify its zeros.

2

Factor g(x)=x2−6x−27g(x) = x^2 - 6x - 27. Enter the two zeros separated by a comma (smaller value first).

3

Complete the square for h(x)=x2+6x+2h(x) = x^2 + 6x + 2.

Step 1: Half of 6 is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ; square it to get   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
Step 2: Rewrite: (x+‾)2−‾+2=(x+3)2+‾(x + \underline{\hspace{5em}})^2 - \underline{\hspace{5em}} + 2 = (x + 3)^2 + \underline{\hspace{5em}}.

half of 6:
half squared:
value inside parentheses:
value subtracted:
final constant:
4

Complete the square to rewrite f(x)=x2−10x+18f(x) = x^2 - 10x + 18 in vertex form. Enter the yy-coordinate of the vertex.

5

The function f(x)=−3(x−2)2+12f(x) = -3(x - 2)^2 + 12 is in vertex form. What is the maximum value of ff?

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