2024 Algebra I Bootcamp - Quadratics

Bootcamp: Quadratics

Match

Formula Review! Match the following:

• Standard Form

• Vertex Form

• Factored Form

• Quadratic Formula

• $$y=ax^2+bx+c$$

• $$y=a\left(x-h\right)^2+k$$

• $$y=a\left(x-p\right)\left(x-q\right)$$

• $$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$$

Dropdown

The vertex is at ​

Select answer

. The y-intercept is at ​

Select answer

The x-intercepts (from left to right) are at ​

Select answer

and ​

Select answer

.

Drag and Drop

For the function y = x² + 2x - 8, drag each option to complete each statement.

The vertex of the parabola is ​

Placeholder

. The y-intercept is ​

Placeholder

.

The x-intercepts (from left to right) are ​

Placeholder

and ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

(-1,-9)

(0,-8)

(-4,0)

(2,0)

(1,9)

Graphing

Graph the function using the vertex and an x-intercept:

$$y=x^2-6x+8$$

Multiple Choice

Which function has the largest maximum?

• f(x) = -x² - 10x + 15

• f(x) = -2x² - 3x + 5

• f(x) = x² + 7x +12

• f(x) = 5x² - 2x + 10

Multiple Choice

Factor:
 3x²-17x+10

• (x-5)(3x-2)
• (x+5)(3x+2)
• (3x-5)(x-2)
• (x+5)(3x-2)

Multiple Choice

Solve by factoring:  2x²+ 7x + 6 = 0

• x= 3/2 and x = 2
• x = -3/2 and x = -2
• x = 6 and x = 7
• x = -6 and x = -7

Multiple Choice

Solve by completing the square:
k² − 12k + 23 = 0

• {6 + √13, 6 - √13}
• {-6 + √13, -6 - √13}
• {6 + √59, 6 - √59}
• {-6 + √59, -6 - √59}

Multiple Choice

Solve by completing the square or by using the quadratic formula.

$$w^2+7w+4=0$$  

• $$\frac{-7\pm\sqrt{33}}{2}$$  

• $$\frac{-7\pm\sqrt{65}}{2}$$  

• $$\frac{7\pm\sqrt{33}}{2}$$  

• $$\frac{-7\pm3\sqrt{11}}{2}$$  

Multiple Choice

Solve using the Quadratic Formula:

$$8x^2+4x-16=-x^2$$

• $$\frac{-2\pm3\sqrt[]{37}}{9}$$

• $$\frac{-2\pm2\sqrt[]{37}}{9}$$

• $$\frac{-2\pm\sqrt[]{37}}{9}$$

• $$-2\pm2\sqrt[]{37}$$

Multiple Choice

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

• 2 ft

• 80 ft

• 144 ft

• 64 ft

Multiple Choice

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

• 5 seconds

• 1 second

• 2 seconds

• 3 seconds