1. Which is the best method for solving the quadratic equation? Solve the quadratic equation using the method chosen. Leave all answers in simplest radical form.

Choose each method once.

• Take the square root of each side.

• Factor and use the zero product property.

• Complete the square.

• Use the quadratic formula.

A. x2 = –16x

B. y2 + 6y – 2 = 0

C. 2a2 = 72

D. p2 + 4p = 8

ANSWER:

2. Consider the quadratic function y = –2x2 + 3x + 4.

A. Does the parabola open upward or downward? Explain.

B. Does the vertex lie on, below, or above the x-axis? Explain.

ANSWER:

1. A. Factor and use the zero-product property; x = 0, -16

   B. Use the quadratic formula; y=-3-√11, -3+√11

   C. Take the square root of each side; x = -6, 6

   D. Complete the square; p= -2(√3 + 1). 2(√3 - 1)

2. A. Downward; coefficient of x² is negative

    B. Above; k is positive

Step-by-step explanation:

1. A. x² = –16x

Factor and use the zero-product property

B. y² + 6y – 2 = 0

Use the quadratic formula

a = 1; b = 6; y = -2

C. 2a² = 72

Take the square root of each side.

D. p² + 4p = 8

Complete the square.

2. y = –2x² + 3x + 4

a = -2; b = 3; c = 4

A. Direction of opening

The parabola opens downward because the coefficient of x² is negative.

B. Vertex

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) are coordinates of the vertex.

The vertex will be above. on, or below the x-axis if k is positive, zero, or negative.

The vertex is above the x-axis because k is positive.  

The graph below shows that your parabola opens downward and the vertex is above the x-axis.

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step-by-step explanation:

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