Exploring Quadratics

The equation 2x²-5x=-12 is rewritten in the form of 2(x-p)²+q=0.  What is the value of q?

• 167/16
• 71/8
• 25/8
• 25/16

Tags

CCSS.HSA-REI.B.4B

Which of the following quadratic functions has complex roots x=-2+3i and x=-2-3i?

• x²+4x-5
• x²-4x-5
• x²-4x+13
• x²+4x+13

Tags

CCSS.HSA.APR.B.3

What are the solutions of the quadratic equation below?
x²-4x-6=0

• x=2±√2
• x=-2±√2
• x=2±√10
• x=-2±√10

Tags

CCSS.HSA-REI.B.4B

Which quadratic function has 3 as its only root?

• x²-9
• x²+9
• x²-6x+9
• x²+6x+9

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

What are the solutions to 3(x-9)²=-180?

• -9±2i√15
• -9±4i√15
• 9±2i√15
• 9±4i√15

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Which graph of the functions below is wider than f(x)=13x²+3?

• g(x)=14x²+3
• g(x)=13x²+5
• g(x)=12x²+3
• g(x)=23x²+3

Given the function f(x)=x²+10x+20, what would change if the function was changed to f(x)=x²+10x+30?

• the vertex
• the line of symmetry
• the shape of the parabola
• the direction the parabola opens

Which statement is true regarding the vertex of the quadratic function f(x)=-(x-4)²+6?

• The vertex is the point (4,6)
• The vertex is the point (-4,6)
• The vertex is located in quadrant 3
• The vertex is located in quadrant 4

The heights of two different projectiles after they are launched are modeled by f(x) and g(x).  The function f(x) is defined as f(x)=-16x²+42x+12.  g(x) is represented by (0,9), (1,33), and (2,25).  What is the approximate difference in the maximum heights achieved by the two projectiles?

• 0.2
• 3.0
• 5.4
• 5.6

The graph of f(x)=x² will be translated 5 units up and 2 units to the right.  Which function describes the graph produced by the translation?

• g(x)=x²-4x+9
• g(x)=x²+4x-1
• g(x)=x²-10x+27
• g(x)=x²+10x+23