Download The Quadratic Formula

Warm-Up #50
11/1/16
1. Solve 6x2 - 24x - 36 = 0 by completing the square.
2. Write the quadratic function y = x2 + 4x - 7 in vertex
form. Identify the vertex and y-intercept.
Only ONE
paper will be
collected from
each group.
Solve each equation by completing the square.
Completing the Square Group Practice
1. x2 + 14x = -20
2. 4x2 + 16x - 24 = 0
3. x2 + 18x - 19 = 0
Write each function in vertex form. Identify the vertex.
4. y = x2 + 6x - 7
5. y = x2 - 2x + 5
Quadratic Functions and Equations Handout
Quadratic Functions and Equations Handout
1. Vertex: (2, 5); Axis of Symmetry: x = 2; Max Value at 5;
6. Vertex: (0, 0); Focus: (0, -1); Directrix: y = 1
Domain: All real numbers; Range: y ≤ 5
7.
2. 106.3 thousand units
3. Vertex: (-1, 5); Axis of Symmetry: x = -1; Max Value at 5;
a. 2 Solutions: x = 0, x = 4
b. 2 Solutions: x = 3, x = -4/3
Domain: All real numbers; Range: y ≤ 5
4. y = 1.5(x - 3)2 - 9.5
5. Directrix: y = 6; y = -⅛(x + 3)2 + 4
Warm-Up #51
11/2/16
2
1. Solve 5x - 45 = 0 by finding square roots.
2. Solve x2 + 10x - 1 = 0 by completing the square.
3. Write the quadratic function y = x2 + 8x - 2 in vertex
form. Identify the vertex and y-intercept.
The Quadratic Formula
Section 4-7
11/2/16
EQ: How can you use different ways to solve a quadratic equation
2
+ + = 0, including a formula that gives values of x in terms of
a, b, & c?
Quadratic Equations
Given ax2 + bx + c = 0, solve by completing the square.
So far, we’ve talked about three different ways to solve
quadratic equations.
1. Finding square roots
2. Factoring
3. Completing the square
Today, we’re going to learn a fourth method:
Using the Quadratic Formula
Quadratic Formula
The Quadratic Formula
Warm-Up #52
Solve each quadratic equation using the quadratic
formula. Note: One side of the equation must equal 0.
Solve each quadratic equation by using the Quadratic
Formula.
1. x2 - 6x - 11 = 0
4. 2x2 + 4x = 8
1. x2 + 8x + 12 = 0
2. 2x2 + 7x - 15 = 0
5. x2 + 6x = -11
2. -4x2 + 20x - 25 = 0
3. x2 + 6x + 9 = 0
6. 3n2 - 8n - 2 = 0
3. 6x2 + 3x = -10
11/3/16
Applying the Quadratic Formula: Fundraising
How many solutions are there?
Your school’s jazz band is selling CDs as a fundraiser. The
total profit p depends on the amount x that your band
charges for each CD. The equation p = -x2 + 48x - 300
models the profit of the fundraiser. What is the least
amount, in dollars, you can charge for a CD to make a
profit of $200?
Solve your assigned problem using the Quadratic
Formula.
Part A has 2 real solutions
A. 2x2 - 5x + 1 = 0
Part B has 1 real solution
The least amount you can charge is $15.28 for each CD.
The Discriminant
To determine the number of real number solutions of a
quadratic equation, find the value of the discriminant,
b2 - 4ac, and use the following information:
b2 - 4ac is positive
b2 - 4ac is zero
b2 - 4ac is negative
2 real solutions
1 real solution
0 real solutions
Determine the number of real solutions.
7. 5x2 - 7x - 8 = 0
8. 9x2 + 24x + 16 = 0
B. x2 - 10x + 25 = 0 Part C has no real solutions
C. x2 + 4x + 8 = 0
To determine the number of
real number solutions, look at
the discriminant: b2 - 4ac