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/ zeroes/ roots
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
In which year did the US declare independence from Britain?
1776
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
What is the smallest planet in the solar system?
Mercury
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, completing the square, and factoring will give you different results when solving a quadratic equation.
False
What fictional city does the popular character Batman live in?
Gotham
Solve the following quadratic equation by factoring.
x2 - 6x - 27 = 0
x = 9 x = -3
Why is the quadratic formula said to be more useful for solving quadratic equations than factoring?
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, roots, zeroes
What is the quadratic formula?
x=(-b +- sqrt(b^2-4ac))/(2a)
Which artist painted the famous "Starry Night" painting?
Vincent Van Gogh
Solve the following quadratic equation by factoring. 2x2 - 5x - 3 = 0
x = -1/2 x = 3
How do we know how many solutions a quadratic function will have when using the quadratic formula?
Look at the discriminant [b^2-(4ac)] (i.e. the number under the square root)
d>0....Two Solutions
d=0....One Solution
d<0....No real solution
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.
ax^2+bx+c=0
What is a tornado called when it forms over water?
Waterspout