Quiz about Rewriting Quadratic Functions

Question 1

Write the following in vertex form:

Accepted Answer

$$\left(x-2\right)^2+2$$

Answer

$$\left(x+2\right)^2$$

Answer

$$\left(x+2\right)^2+2$$

Answer

$$\left(x+2\right)^2-2$$

Question 2

Rewrite in vertex form: $$f\left(x\right)=x^2+8x+18$$

Accepted Answer

$$\left(x+4\right)^2+2$$

Answer

$$\left(x+4\right)^2+14$$

Answer

$$\left(x+8\right)^2-46$$

Answer

$$\left(x+4\right)^2-14$$

Question 3

Write in vertex form: $$f\left(x\right)=x^2+2x-1$$

Accepted Answer

$$f\left(x\right)=\left(x+1\right)^2-2$$

Answer

$$f\left(x\right)=\left(x+1\right)^2$$

Answer

$$f\left(x\right)=\left(x-1\right)^2$$

Answer

$$f\left(x\right)=\left(x+1\right)^2+2$$

Question 4

Rewrite in vertex form: $$f\left(x\right)=x^2+5x+9$$

Accepted Answer

$$f\left(x\right)=\left(x+\frac{5}{2}\right)^2+\frac{11}{4}$$

Answer

$$f\left(x\right)=\left(x+\frac{5}{2}\right)^2+9$$

Answer

$$f\left(x\right)=\left(x+5\right)^2-16$$

Answer

$$f\left(x\right)=\left(x+5\right)^2+9$$

Question 5

Rewrite in standard form:
y=(x-7)²

Accepted Answer

y = x²-14x+49

Answer

y = x2-49

Answer

y = x2+49

Answer

y = x²-14x-49

Question 6

Write a quadratic equation given the x intercepts and one other point.

Step 1: Write the factors.

The intercepts of this function are (6, 0) and (8, 0). Write the factors.

Accepted Answer

(x-6) and (x-8)

Answer

(x+6) and (x+8)

Answer

(x-6) and (x+8)

Answer

(x+6) and (x-8)

Question 7

Write a quadratic equation given the x intercepts and one other point.

Step 1: Write the factors.

The intercepts of this function are (6, 0) and (8, 0). Write the factors.

Accepted Answer

(x-6) and (x-8)

Answer

(x+6) and (x+8)

Answer

(x-6) and (x+8)

Answer

(x+6) and (x-8)

Question 8

Write the equation of the quadratic if it goes through (-1, 2) and has the given intercepts.

Accepted Answer

y = 2/5 (x-0)(x-4)

Answer

y=5/2 (x-0)(x-4)

Answer

y= 2/3 (x-0)(x-4)

Answer

y= 3/2 (x-0)(x-4)

Question 9

Rewrite in vertex form: $$f\left(x\right)=2x^2+4x-2$$

Accepted Answer

$$f\left(x\right)=2\left(x+1\right)^2-4$$

Answer

$$f\left(x\right)=\left(x+2\right)^2-6$$

Answer

$$f\left(x\right)=2\left(x+2\right)^2-6$$

Answer

$$f\left(x\right)=2\left(x+1\right)^2-6$$

Question 10

Rewrite in vertex form:

Accepted Answer

$$f\left(x\right)=-2\left(x-1\right)^2-1$$

Answer

$$f\left(x\right)=-2\left(x+1\right)^2-1$$

Answer

$$f\left(x\right)=-2\left(x-2\right)^2-1$$

Answer

$$f\left(x\right)=-2\left(x+2\right)^2+5$$

Question 11

Rewrite the quadratic functions in vertex form.

Accepted Answer

$$f\left(x\right)=-2\left(x+2\right)^2+1$$

Answer

$$f\left(x\right)=2\left(x-2\right)^2+1$$

Answer

$$f\left(x\right)=-2\left(x-8\right)^2+7$$

Answer

$$f\left(x\right)=2\left(x+8\right)^2-7$$

Question 12

Rewrite the quadratic functions in standard form. $$f\left(x\right)=-\left(x+2\right)^2+17$$

Accepted Answer

$$f\left(x\right)=-x^2-4x+13$$

Answer

$$f\left(x\right)=2x^2+x-17$$

Answer

$$f\left(x\right)=x^2+2x+17$$

Answer

$$f\left(x\right)=x^2+4x-13$$

Question 13

Rewrite the quadratic functions in vertex form.
$$f\left(x\right)=3x^2+6x-4$$

Accepted Answer

$$f\left(x\right)=3\left(x-1\right)^2-7$$

Answer

$$f\left(x\right)=3\left(x+1\right)^2+7$$

Answer

$$f\left(x\right)=4\left(x+6\right)^2+3$$

Answer

$$f\left(x\right)=-4\left(x-6\right)^2+3$$

Question 14

Rewrite the quadratic functions in vertex form.

$$f\left(x\right)=x^2-2x-3$$

Accepted Answer

$$f\left(x\right)=\left(x-1\right)^2-4$$

Answer

$$f\left(x\right)=\left(x+2\right)^2-3$$

Answer

$$f\left(x\right)=\left(x+2\right)^2+3$$

Answer

$$f\left(x\right)=\left(x+2\right)^2+4$$

Question 15

Rewrite $$y=x^2\ -6x\ +8$$ into vertex form

Accepted Answer

y=(x-3)²- 1

Answer

y=(x-3)²+ 2

Answer

y=(x-3)²- 8

Answer

y=(x-3)² + 8

Rewriting Quadratic Functions

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