Factoring
Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0
x = -2, 7
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?
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:
y = x2+6x+9
Factoring
Solve the following quadratic equation by factoring. x2+3x+2 = 0
x = -2, -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:
y= 5x2+2x-2
Quadratic Formula
Solve the following quadratic equation by factoring. x2 - 6x + 5 = 0
x = 1, 5
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. Also provide the formula.
Axis of Symmetry; x= -b/2a
True or false?
Using the quadratic formula and factoring will give you different results.
False
What is the discriminant when there is only one root?
Solve the following quadratic equation by factoring.
x2 - 6x - 27 = 0
x = -3, 9
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 x-intercepts, zeros, critical values, and ___________ .
roots
What is the quadratic formula? (Sing it for extra points.)
x=(-b +- sqrt(b^2-4ac))/(2a)
y= a(x-h)^2+k
Solve the following quadratic equation by factoring. 2x2 - 5x - 3 = 0
x = -1/2, 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. (the number under the square root)
This point is AKA the "turning point" 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.
How will the graph of a quadratic look if the first coefficient is negative?
concave down / reflected across the x-axis