Factoring
Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0
x = 7 x = -2
or x = { 7, -2}
When solving quadratic equations, we are trying to find what feature of the parabola?
x-intercepts
What is the name of the graph for quadratic equations?
A parabola
Identify a, b and c in the following equation:
x2 + 6x + 5 = 0
a = 1; b = 6; c = 5
Find the best method for solving the quadratic equation below:
x2+6x+9 = 0
Factoring
Solve the following quadratic equation by factoring. x2+3x+2 = 0
x = -2 x = -1
What are the three different types of solutions we can have when solving quadratics
No real solution (Imaginary), One solution or Two solutions
This is the point where a quadratic function crosses the y-axis
y-intercept
Identify a, b and c in the following equation:
x2 - 9x + 20 = 9
a = 1; b = -9; c = 11
Find the best method for solving the quadratic equation below:
5x2+2x-2 = 0
Quadratic Formula
Solve the following quadratic equation by factoring. x2 - 6x + 5 = 0
x = 5 x = 1
How do we know a quadratic function does not have solutions when looking at a graph?
It does not touch or pass through the x-axis
This line crosses the vertex of a parabola and divides the parabola into 2 equal halves.
Axis of Symmetry
True or false?
Using the quadratic formula and factoring will give you different results.
False
What is the shape of a parabola?
A "u" shape
Solve the following quadratic equation by factoring.
x2 - 6x - 27 = 0
x = 9 x = -3
Why is the quadratic formula useful for solving quadratic equations?
We can ALWAYS use the quadratic formula, but we cannot always factor.
Another name for the solutions to a quadratic equation are its ___________ .
roots
What is the quadratic formula?
x=(-b +- sqrt(b^2-4ac))/(2a)
What equation do you use to find the axis of symmetry?
x=-b/2a
Solve the following quadratic equation by factoring. 2x2 - 5x - 3 = 0
x = -1/2 x = 3
How do we know a quadratic function does not have a real number solution when using the quadratic formula?
The discriminant will be negative. (i.e. the number under the square root)
This point is the center of a parabola and can be a maximum or minimum, depending on the direction of the parabola.
Vertex
What is the first step for solving an equation using the quadratic formula?
Make sure the equation is in standard form, which means it should equal 0.
(Also, evaluate the discriminant)
When graphing quadratic equations, how will the graph look like if the first coefficient is a negative number?
Upside down 'U'