Solve
Solve (x-7)(x+2)
x^2-5x-14
x- intercepts
This is the point where a quadratic function crosses the y-axis
y-intercept
Identify a, b and c in the following equation: 3x^2+4x+1=0
a=3 b=4 c=1
Is this a quadratic equation? x^2+6x+9=0
Yes
Solve x^2+3x+2=0
x=-2 and x=-1
What are the three different types of solutions we can have when solving quadratics?
No solution, One solution or Two solutions
This point is the center of a parabola and can be a maximum or minimum, depending on the direction of the parabola
Vertex
Identify a, b and c in the following equation: x^2+6x+5=0
a=1 b=6 c=5
Is this a quadratic equation? y=9x^3+x^2-x+8
No
x=5 and x=1
How do we know a quadratic function does not have solutions when looking at a graph?
It does not touch the x-axis
This line crosses the vertex of a parabola and divides the parabola in half
Identify a, b and c in the following equation: x^2-9x+20=9
a=1 b=-9 c=11
Solve the following x^2-5x-24=0
x=8 and x=-3
Solve x^2-6x-27=0
x=9 and x=-3
Why is the quadratic formula useful for solving quadratic equations?
We can always use the quadratic formula, but we cannot always factor
Factored
Solve the following quadratic equation by finding the solutions: 2x^2+9x+4=0
x= -1/2 and x=-4
x=-3.63 and x=-5.36
Solve 2x^2-5x-3=0
x=-1/2x and x=3
How do we know a quadratic function does not have solutions when using the quadratic formula?
There will be a negative number under the square root
When solving quadratic equations, what is another name for x-intercepts
Solutions, Roots, Zeros of a function
Solve the following quadratic equation by finding the roots: 4x^2-17x-15=0
x=5 and x=-3/4
x=8 and x=-6