18-20 QuadraticFactoring Flashcards
What is a Quadratic equation?
An equation with 2 as the highest power.
Why is it called quadratic?
Quad refers to squaring.
What is the standard form of a Quadratic Equation?
y = ax² + bx + c
What is the shape of a graph of a Quadratic equation?
a parabola
because of the square
What does a tell you in
y = ax² + bx + c
If a is positive, the parabola points up.
If it is negative, it points down.
Also, the larger a is, the tighter the parabola.
How many x-intercepts are there with a quadratic equation?
0, 1 or 2
It has 0 if it above the x-axis.
It has 1 if it sits on the x-axis.
It has 2 if it sits below the x-axis.
How can you expand the following into a quadratic equation:
5x(8x - 3)
40x² - 15x
What is the opposite of expanding an equation?
Factoring - finding the linear roots of a quadratic equation.
This can be called the Greatest Common Factor.
What is the Greatest Common Factor of
10x² + 20x - 40?
= 10(x² + 2x - 4)
What is the FOIL method for expanding?
(x + 5)(x - 3)
First, Outside, Inside, Last
x² - 3x + 5x -15
x² + 2x - 15
In reverse, factor:
x² + 2x - 15
(x + 5)(x - 3)
What type of equation is
(x² - 49) and how do you solve it?
Difference of 2 squares.
(x + 7)(x - 7)
What does factoring a quadratic equation tell you about its graph?
It gives you the x-intercepts (where y = 0)
What are the x-intercepts of
y = x² - 8x + 7
y = 0 when:
y = (x - 7)(x - 1)
either x = 7 and x = 1
What are the x-intercepts of
y = x² + 9x + 20?
y = (x + 4)(x + 5)
y = 0 when x = -4 and x = -5
