Quadratic Functions

The cost to produce a product is modeled by the function f(x) = 5x² − 70x + 258, where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.

• f(x) = 5(x − 7)² + 13; The minimum cost to produce the product is $7.

• f(x) = 5(x − 7)² + 13; The minimum cost to produce the product is $13.

• f(x) = 5(x − 7)² + 258; The minimum cost to produce the product is $7.

• f(x) = 5(x − 7)² + 258; The minimum cost to produce the product is $258.

• x = -5, -1

• x = -11, -7

Tags

CCSS.HSA-REI.B.4B

How can you tell when a quadratic equation has no real solutions?

• When the radicand (the value inside the square root) equals zero

• When the radicand (the value inside the square root) is negative

• When the radicand (the value inside the square root) is not a perfect square

• When the b-value in the quadratic equation is greater than the value in the radicand (the value inside the square root)

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Use the quadratic formula to find the exact solutions of x² = 4 − 7x.

Tags

CCSS.HSA-REI.B.4B

Use the quadratic formula to find the approximate solutions of 4x² + 3 = -12x. Round the solutions to the nearest hundredth.

• x ≈ 0.28, 2.72

• x ≈ -0.23, 3.23

• x ≈ -2.72, -0.28

• x ≈ -3.23, 0.23

Tags

CCSS.HSA-REI.B.4B

Alexei wants to hang a mirror with a frame around it. The mirror and frame must have an area of 19.25 square feet. The mirror is 3 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

• (x - 3)(x - 5) = 19.25

• (x + 3)(x + 5) = 19.25

• (2x - 3)(2x - 5) = 19.25

• (2x + 3)(2x + 5) = 19.25

What is the axis of symmetry of this parabola?

• -4

• x = -4

• x = -2

• y = -4

Tags

CCSS.HSF-IF.C.7A

Identify the function graphed here.

Tags

CCSS.HSF-IF.C.7A

Identify the function graphed here.

Tags

CCSS.HSF-IF.C.7A

What is the y-intercept of this parabola?

• (6, 0)

• (-2, 0)

• (-4, -2)

• (0, 6)

Tags

CCSS.HSF-IF.C.7A