Graphing Quadratics Terms

Determine the vertex from the following equation: -\left(x+1\right)^2-1

• Vertex: (1,-1)

• Vertex: (-1, 1)

• Vertex: (-1, -1)

• Vertex: (1, 1)

• Narrow

• Wider

Identify the a, h, and k terms in the following equation: 2\left(x+4\right)^2-1

• a=2, h=-4, k=-1

• a=-2, h=4, k=1

• a=2, h=4, k=1

• a=-2, h=-4, k=1

For each function, identify the vertex, y-intercept, x-intercept(s), and axis of symmetry. Identify whether the function has a maximum or minimum and give its value. f(x) = -x^2 + 4x + 5.

• Vertex: (2, 9), y-intercept: 5, x-intercepts: (5, 0) and (-1, 0), axis of symmetry: x = 2, maximum value: 9

• Vertex: (2, 9), y-intercept: 5, x-intercepts: (1, 0) and (5, 0), axis of symmetry: x = 2, maximum value: 9

• Vertex: (2, 9), y-intercept: 5, x-intercepts: (0, 0) and (4, 0), axis of symmetry: x = 2, maximum value: 9

• Vertex: (2, 9), y-intercept: 5, x-intercepts: (2, 0) and (3, 0), axis of symmetry: x = 2, maximum value: 9

What are the coordinates of the vertex? Is it a maximum or a minimum?

• (2, 3); minimum

• (2, 5); maximum

• (2, 3); maximum

• (2, -3); minimum

• (2, -3); maximum

Answer explanation

What is the axis of symmetry?

• x=2

• x=3

• y=2

• y=-3

Answer explanation

Axis of symmetry is the vertical line that goes through the vertex. Since the vertex is (2, 3), the axis of symmetry is x=2.

On what interval of x is the graph decreasing?

Answer explanation

The graph decreases after the maximum at x=2 so x > 2 is the interval that the graph is decreasing.

Tags

CCSS.HSF-IF.C.7A

On what interval of x is the graph increasing?

Answer explanation

The graph increases before the maximum at x=2 so x < 2 is the interval that the graph is increasing.

Tags

CCSS.HSF-IF.C.7A

Write a quadratic function that models T(x), the total cost of the tickets for a group with x people.

• T(x) = -x^2+46x

• T(x) = x(46-x)

• T(x) =46-x

• T(x) = 46x^2 + x

What is the vertex of this quadratic equation?  
y = 2(x - 2)²  +  5

• (-2,5)

• (2,5)

• (5,-2)

• (-5,-2)