Unit 7 Review

Unit 7 Review

Introduction to Quadratic Functions

Multiple Choice

Standard form of a quadratic equation

• y=x²

• y=ax²+bx+c

• y=mx+b

• y=x

Multiple Choice

Quadratic equations take the shape of a _______ when graphed.

• U

• straight line

• wavey line/snaked

• circle/elliptical

Multiple Choice

Which letter determines if a parabola opens up or down?

• a

• h

• k

Multiple Choice

The vertex of this quadratic is...

• (1,16)
• (-3,0)
• (5,0)
• (0,15)

Multiple Choice

The line that goes through the vertex of a parabola is called the...

• Vertex
• Axis of Symmetry
• x-intercept
• y-intercept

Multiple Choice

What is the equation for axis of symmetry?

• y=3
• x=3
• x=5
• x=1

Multiple Choice

What is the axis of symmetry for this graph?

• y=2
• x=2
• x=0
• y=0

Multiple Choice

What is the green dashed line called?

• roots or x-intercepts
• parabola
• axis of symmetry
• line of dashes

Multiple Choice

Does this graph have a maximum or minimum?

• Minimum
• Maximum

Multiple Choice

Find the vertex  y = x² - 2x - 5

• V(-2, 10)
• V(-1, 15)
• V(1, -6)
• V(1, -12)

Multiple Choice

Find the vertex.  y = x²+ 16x + 71

• V(-8, 7)
• V(-8, 3)
• V(8, 10)
• V(16, -2)

Multiple Choice

What is the green dot on the parabola called?

• maximum
• minumum
• roots
• zeros

Multiple Choice

What is the first step in solving 
(x + 2)(x - 3) = 0      ?

• Plug in zero for x
• Solve for x
• FOIL
• Set each binomial factor equal to zero

Multiple Choice

Solve
x² + 2x - 24 = 0

• x = -6, x = 4
• x = 6, x = -4
• x = 12, x = -2
• x = 8, x = -3

Multiple Choice

Standard form of a quadratic equation

• y=x²
• y=ax²+bx+c
• y=mx+b
• y=x

Multiple Choice

Solve:  $3x^2+7x-6=0$ 

•  $x\ =\ 3$  and  $x=-\frac{2}{3}$  

•  $x=-3$  and  $x=\frac{2}{3}$  

•  $x=-3$  and  $x=-\frac{2}{3}$  

•  $x=3$  and  $x=\frac{2}{3}$  

Multiple Choice

Solve:   $4x^2+15x+14=0$  

•  $x=\frac{7}{4}$  and  $x=2$  

•  $x=-\frac{7}{4}$  and  $x=2$  

•  $x=\frac{7}{4}$  and  $x=-2$  

•  $x=-\frac{7}{4}$  and  $x=-2$  

Multiple Choice

Solve by taking square roots.
 $x^2-64=0$  

•  $\left\{\pm\ 32\right\}$  

•  $\left\{\pm\ 16\right\}$  

•  $\left\{\pm\ 8\right\}$  

•  $\left\{\pm\ 4\right\}$  

Multiple Choice

Find the x-intercept(s) by taking square roots.
 $\left(x-1\right)^2=6$  

•  $\left\{\pm\sqrt{6}-1\right\}$  

•  $\left\{1\pm\sqrt{6}\right\}$  

•  $\left\{37\right\}$  

•  $\left\{1\pm\sqrt{3}\right\}$   

Multiple Choice

Solve by taking square roots.
 $\left(x-14\right)^2=36$  

•  $\left\{20\right\}$  

•  $\left\{8,\ 20\right\}$  

•  $\left\{-8,\ -20\right\}$  

•  $\left\{-22\right\}$  

Multiple Choice

Solve by taking square roots.
 $x^2-225=0$  

Hint: Isolate $x^2.$   

•  $\left\{\pm\ 14\right\}$  

•  $\left\{15\right\}$  

•  $\left\{\pm\ 15\right\}$  

•  $\left\{112.5\right\}$  

Multiple Choice

Solve by taking square roots.
 $x^2=81$  

•  $\left\{40.5\right\}$  

•  $\left\{9\right\}$  

•  $\left\{\pm\ 9\right\}$  

•  $\left\{0,\ 9\right\}$  

Multiple Choice

Solve the following quadratics equation by completing the square...

x² + 2x - 10 = 0

• x = -1 ± √11

• x = 1 ± √11

• x = 11 ± √1

• x = -11 ± √1

Multiple Choice

Solve the following quadratics equation by completing the square...

x² + 12x + 10 = 0

• x = -6 ± √26

• x = 6 ± √26

• x = 26 ± √6

• x = -26 ± √6

Multiple Choice

Solve by completing the square. Round.
x² -4x = 5

• 11 and -7
• 1 and 3
• 1.73 and -1.73
• 5 and -1

Multiple Choice

What mathematical process did they use?

• Quadratic Formula
• Completing the Square
• Factoring
• Differentiation

Multiple Choice

Solve the following quadratics equation by completing the square...

x² + 4x - 1 = 0

• x = -2 ± √5

• x = -5 ± √2

• x = 2 ± √5

• x = -5 ± √5

Multiple Choice

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

• x = -2 ± √3

• x = -3 ± √2

• x = 2 ± √3

• x = 2 ± √2

Multiple Choice

The length of a rectangle is 4 cm more than its width. The area of the rectangle is 96 sq. cm. Find its dimensions.

• 4 cm by 8 cm

• 6 cm by 10 cm

• 8 cm by 12 cm

• 10 cm by 14 cm

Multiple Choice

Your cousin hit a golf ball with an initial velocity of 27 feet per second. The equation h = -6t² + 27t models the golf ball's height in feet t seconds after the ball was hit. How long after being hit did the ball reach maximum height?

• 1 second

• 2.25 seconds

• 3 seconds

• 4.5 seconds

• 5 seconds

Multiple Choice

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

• 2.625

• 6.25

• 100

• 200

• 210.25

Multiple Choice

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation

h = -2t² + 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

• 2

• 4

• 9

• 10

• 15

Multiple Choice

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

• 0.1 seconds

• 0.25 seconds

• 0.50 seconds

• 0.75 seconds

• 1 second

Multiple Choice

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h = -4t² + 2t models her jump where h is her jump's height in feet t seconds after the mummy scares her. When did she reach her maximum height?

• 0.1 seconds

• 0.25 seconds

• 0.50 seconds

• 1 second

• 2 seconds

Multiple Choice

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

• 1 foot

• 5 feet

• 7 feet

• 8 feet

• 12 feet

Multiple Choice

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t² + 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

• 0.5 seconds

• 1 second

• 1.5 seconds

• 2 seconds

• 3 seconds

Multiple Choice

The length of a rectangle is 1 m longer than 3 times its width. The area is 80 m² . Find the dimensions of this rectangle.

• 4m by 13m

• 5m by 16m

• 6m by 19m

• 7m by 22m