Warm- Up February 261. What is the vertex, axis of symmetry,

max./min, y-intercept, and direction of opening of the following y = -2x2 – 8x – 3.

2. Find the solutions of the following by graphing. y = 3x2 + 6x + 2

3. A baseball is thrown into the air. Its height h, in feet, after t seconds given by the function h = - 16t2 + 30t + 6. How long will it take the ball to reach its maximum height? What is the ball’s maximum height?

Factoring to Solve Quadratics

When a quadratic equation is set up like this and equal to zero

(x + 3)(x + 2) = 0

You can break it up to solve x + 3 = 0 and x + 2 = 0

Example1. (4t + 1) (t – 2) = 0

2. (2x + 3) (x – 4) = 0

You Try

1. (x + 1) (x – 5) = 0 2. (2y + 1) (y + 14) = 0

3. (7n – 2) (5n – 4) = 0

Let’s quickly review types of problems we have factored.

1. x2 + 5x + 6

2. 2x2 + 6x + 4

3. 9x2 – 49

4. 4x3 + 8x2 + 3x + 6

5. 6x4y + 36x2y4

Short Trinomials

Examples:1. x2 + 8x + 15 = 0 2. m2 – 5m – 14 = 0

Short Trinomials

You Try: 3. p2 + p – 20 = 0 4. x2 – x – 6 = 0

Long TrinomialsExample: 5. 2a2 – 15a + 18 = 0

Long Trinomials

You Try:6. 2z2 – 21z – 36 = 0

Quadratics must be in Standard Form before you can factor.

ax2 + bx + c = 0Examples:

1. 4x2 – 21x = 18

You Try

2. x2 + 14x = -49

Examples

1. c2 = 5c 2. x3 – 3x2 = 18x

Example

3. 9b2 = 16

You Try 1. x2 = 6x 2. x3 + 13x2 = -42

3. 36x2 - 49

A box shaped like a rectangular prism has a volume of 280 in.3. Its dimensions are 4 in by (n + 2)in. by (n + 5)in. Find n.

You are constructing a frame for the rectangular photo shown. You want the frame to be the same width all the way around and total area of the frame and the photo to be 315 in.2. What should the outer dimensions of the frame be?