3. Quadratic Equations: (Write this down)
Class Notes:
1. Have a highest degree of 2.
2. Have a standard form of: ax2 + bx + c = 0
3. Have a graph which always results in a parabola.
4. Have solutions which
show the x intercept(s)
Solve: x2 + 3x - 4 = 0
(x ) (x ) = 0+ -4 1
x = (-4, 1)
x2 = 25, 4y2 + 2y - 1 = 0, y2 + 6y = 0, x2 + 2x - 4 = 0
The following are all examples of
quadratic equations:
4. A). The graphs of quadratics are not straight lines, they are always in
the shape of a Parabola.
B) Parabolas ALWAYS have two solutions.
C) The slope of a quadratic is not constant. The slope-intercept
formula will not work with parabolas.
What about (x – 4)2
?
These are referred to as repeated solutions.
Find the solutions to this quadratic equation.
D) The solutions of a equation are also called the roots of the equation.
Quadratic Equations
9. Solving Quadratic Equations by Factoring
Let's look at some of the different types of equations
you'll face and how to deal with each of them
1: Set the equation = to 0 and solve:
Example A. x2 + 6x + 9
x2 + 6x + 9 = 0; (x + 3) (x + 3) = 0, x = -3.This is a perfect square
trinomial, and the parabola only touches the x axis at -3 and
would be in this shape:
-3
10.
11. Solving Quadratic Equations by Factoring
2. Solve x2 = 64. Remember the standard form?
ax2 + bx + c = 0, where only a cannot = 0
In this case, b is 0, and c is 64.
We can solve by taking the square root of both sides.
3. Solve: 2x2 - x = 3
Place all terms to the left of the = sign (Standard Form).
The result is x = + 8; x = 8, and x = -8
4. Solve: x2 = 5x ***Do not cancel an 'x' from each side.
Factor GCF first, then solve
12. Take 5, then we'll begin the test:
Please Clear Your Desks/Tables of everything
Except scratch paper, pencil, calculator.
You will need:
Your correct code, pencil only, no phones.,
scratch paper
You can use a regular calculator, but one is
not necessary for this test.
