Quadratic Formula and Spiral Review

Notes: Solving Using Quadratic Formula

Multiple Choice

Factor out the GCF.

21m² - 14

• 7(3m² - 2)

• 21(m² - 2)

• 14(1.5m² + 1)

• 7(3m² + 2)

Multiple Choice

Factor out the GCF.

2m² - 18m

• 2(m² + 9m)
• 2m(m - 9)

• m(2m - 18)
• 2(m² - 18m)

Multiple Choice

Factor the difference of squares.

49x² – 9

• (7x - 3)(7x + 3)
• (7x - 9)(7x + 9)
• (49x - 3)(49x + 3)
• (7x - 1)(7x + 1)

Drag and Drop

Factor the trinomial.

10x² – 11x + 3

Factors: (​

Placeholder

x - 3)(​

Placeholder

x - ​

Placeholder

)

Drag these tiles and drop them in the correct blank above

5

2

1

6

Multiple Choice

Factor the perfect square trinomial.

w² + 16w + 64

• (w + 8)²
• (w - 8)²
• (w + 16)(w + 4)
• (w + 4)²

Multiple Select

Solve for x.

x² – 4 = 0

• 2

• -2

• 4

• -4

Multiple Choice

Solve for x.

3(x – 1)² + 5 = 26

• 2 ± √5

• -1 ± √7

• 3 ± √3

• 1 ± √7

• -3 ± √3

Multiple Choice

Solve for x.

5(x² – 10) – 3 = 27

• {-4, 4}

• {-1, 1}

• {-5, 5}

• {-3, 3}

• {-2, 2}

Drag and Drop

If A√B is the simplified form of √−882, what are the values of A and B?

​

Placeholder

√​

Placeholder

Drag these tiles and drop them in the correct blank above

21i

2

21

63i

3

7

18

2i

Quadratic Formula Steps

4. Plug a, b, and c into the Quadratic Formula
5. Simplify the square root
6. Simplify the fraction

1. Put equation in standard form
2. Divide out the GCF
3. Identify coefficients a, b, and c

​State the two solutions.

Labeling

10. Plug into the quadratic formula.

3x² - 6x + 8 = 0

Drag labels to their correct position on the image

-6

6

3

3

8

6

-6

Multiple Choice

Solve for x.

2x² – 4x – 48 = 0

• x = -6, x = 4

• x = 8, x = 12

• x = 6, x = -4

Multiple Choice

Solve for x.

x² + 2x + 1 = 12

• x = 1 ± √3
• x = -1 ± 2√3
• x = -2 ± √3
• x = ± 3

Multiple Choice

Solve for x.

−x² + 4x = 13

• 5 ± 2i
• -1 ± 4i
• 3 ± 1i
• 2 ± 3i

Multiple Choice

Simplify the expression.

(7 + 2i) + (9 – 5i)

• 10 + 7i
• 5 - 3i
• 16 - 3i

Multiple Choice

Find product of the factors.

(6i)(2 + 3i)

• 12 + 18i
• -12 - 18i
• 18i² + 8i

• -18 + 12i

Multiple Choice

Find product of the factors.

(1 – 2i)(3 + 4i)

• 5 + 6i
• -1 + 2i
• 11 - 2i
• 7 - 4i

Multiple Choice

Solve for y.

3x + 4y = 20

• y = 20 - 3x
• y = 4x + 20
• $$y=\frac{3}{4}x-5$$

• $$y=-\frac{3}{4}x\ +5$$

Drag and Drop

Solve the system.

y = 5x + 1

y = 11x – 17

Solution: (​​

Placeholder

,​

Placeholder

)

Drag these tiles and drop them in the correct blank above

3

16

5

6

Multiple Choice

Set up an augmented matrix for the system.

Multiple Choice

Solve the system.

• x = -17, y = 5, z = -6
• x = -5, y = 10, z = 1
• x = 10, y = -5, z = 2
• x = 14, y = -1, z = 8

Multiple Choice

Given the quadratic parent function, 𝑓(𝑥)=𝑥² graph 𝑔(𝑥) that has the following transformations: reflected across the x–axis, vertically stretched by a factor by 4, left 1, and up 3?

Drag and Drop

Given the parent graph (solid) and the new graph (dashed), describe the transformations.

Reflection: ​

Placeholder

Dilation: ​

Placeholder

Horizontal Translation: ​

Placeholder

Vertical Translation: ​

Placeholder

Drag these tiles and drop them in the correct blank above

across x-axis & y-axis

across y-axis

none

vertical compression

vertical stretch

right

left

up

down

across x-axis

Drag and Drop

What transformations occurred from 𝑓(𝑥)=𝑥² to 𝑔(𝑥)=−5𝑓(𝑥+7)−3?

Reflection: ​

Placeholder

Dilation: ​

Placeholder

Horizontal Translation: ​

Placeholder

Vertical Translation: ​

Placeholder

Drag these tiles and drop them in the correct blank above

across y-axis

none

vertical compression

vertical stretch

left

up

down

across x-axis

right

Fill in the Blanks

If $f\left(x\right)=\frac{3}{4}x+5$ , evaluate 𝑓(8).

Multiple Choice

If $$f\left(x\right)=3x^2+4x-5$$ and $$g\left(x\right)=2x+1$$ , evaluate 𝑔(𝑓(−1)).

• 3
• -5
• -6

• -11

Fill in the Blanks

If $f\left(x\right)=\frac{1}{2}x+4$ and $g\left(x\right)=x-1$ , evaluate 𝑓(𝑔(11)).

Drag and Drop

Identify the function type and equation.

Type: ​

Placeholder

Equation: ​

Placeholder

Drag these tiles and drop them in the correct blank above

cube root

y = ∛x

cubic

y = x³

square

square root

y = x²

y = √x

Drag and Drop

Identify the function type and equation.

Type: ​

Placeholder

Equation: ​

Placeholder

Drag these tiles and drop them in the correct blank above

cube root

y = ∛x

cubic

y = x³

square

square root

y = x²

y = √x

Drag and Drop

Identify the function type and equation.

Type: ​

Placeholder

Equation: ​

Placeholder

Drag these tiles and drop them in the correct blank above

cube root

y = ∛x

cubic

y = x³

square

square root

y = x²

y = √x

Drag and Drop

Identify the function type and equation.

Type: ​

Placeholder

Equation: ​

Placeholder

Drag these tiles and drop them in the correct blank above

cube root

y = ∛x

cubic

y = x³

square

square root

y = x²

y = √x

Drag and Drop

Identify the function type and equation.

Type: ​

Placeholder

Equation: ​

Placeholder

Drag these tiles and drop them in the correct blank above

exponential

y = 10^x

rational

y = 1/x

logarithmic

y = log(x)

Drag and Drop

Identify the function type and equation.

Type: ​

Placeholder

Equation: ​

Placeholder

Drag these tiles and drop them in the correct blank above

exponential

y = 10^x

rational

y = 1/x

logarithmic

y = log(x)