QUADRATIC FUNCTIONSMIDTERM EXAM: FEB 1, W, 10-11:30 AM

BAR AND DINING LAB (Bring Calculator)

Lesson 4.2

Real Zeroes

Factoring

Quadratic Formula

Zeroes

• The values of x so that f(x) = 0.

• Real (as opposed to imaginary) zeroes are also the x-intercepts of the function.

Zeroes of Quadratic Functions

CASE 1: FACTORABLE QEs• The Zero Product Theorem

For a product to be equal to zero, at least one of its factors must be equal to zero.

i.e. If abcd = 0, then either a=0 or b=0 or c=0 or d=0.

• To solve (x+2)(x-3)(2x+1)=0, find values of x that will make each factor equal to zero.

• Hence, the solutions are x = -2, 3 and -1/2.

Zeroes of Quadratic Functions

Example 1:

Find the x-intercept/s of f(x) = x2 – 9.

Solution: 0 = x2 – 9

0 = (x – 3)(x + 3)

Hence, x = 3 and -3

Answers to the SW:

1. 0 = 4x2 – 9 0 = (2x + 3)(2x – 3) Solution: x = -3/2 and 3/22. 0 = x2 - 5x – 24 0 = (x – 8)(x + 3) Solution: x = 8, -33. 20 = 9x - x2   0 = - x2 + 9x – 20 = (-x + 4)(x – 5) Solution: x = 4, 54. 0 = 3x2 + 4x – 4 Solution: x = 2/3, -25. 3 = 4x2 + 4x Solution: x = -3/2, 1/2

Quadratic Formula

• Not all quadratic equations are factorable but that does not mean that it does not have zeroes.

• The following formula solves for the value of x that satisfies the equation 0 = ax2 + bx + c:

• Notice that this is actually two formulas, one using + and the other using -

Quadratic Formula

Example: Find the x-intercepts of f(x)=x2 – 3x – 1

Solution: a = 1, b = -3, c = -1

Seatwork

1. Solve for x:

a) 12 = x2 + x c) 2x2 + 6 = 7x

b) 0 = 2x2 – 2x – 3 d) 0 = -x2 + 3x + 5

2. Given the function f(x) = x2 + 8x + 10, do the ff:

a) Find the vertex, y-intercept and x-intercepts

b) Graph f(x) showing the points in (a).

c) Identify the domain, range, axis of symmetry and interval/s where f(x) is positive.