Vocabulary
What is the shape of a quadratic function called?
Parabola
Factor this expression: 0 = x2+2x-3
Then find the x-intercept(s).
(x+3)(x-1)
x = -3; x = 1
Simplify this expression: 0 = (x+1)(x+2)
Find the x-intercept(s).
x2+3x+2
x = -1; x = -2
Find the x-intercept(s) of this equation: 0=x2-9
Be sure your answer is in its simplest form!
x = +3
x = -3
What part of an equation or expression makes it quadratic?
Has a power of 2, ex. x2+x-2
What do we call the highest or lowest point on a quadratic function?
Maximum or minimum; or vertex
Factor this expression: 0 = x2-5x+6
Then find the x-intercept(s).
0 = (x-3)(x-2)
x = 3; x = 2
Simplify this expression: 0 = (x+2)(x-7)
Find the x-intercept(s).
x2-5x-14
x = -2; x = 7
Find the x-intercept(s) of this equation: 0 = x2-72
Be sure your answer is in its simplest form!
x = +6√2
x = -6√2
How many solutions can a quadratic function have?
0, 1, or 2
What do we call the line that cuts a graph of a quadratic function into 2 mirrored pieces?
Axis/line of symmetry
Factor this expression: x2+6x = 0
Then find the x-intercept(s).
x(x+6) = 0
x = 0; x = -6
Simplify this expression: 0 = (x-5)(x+5)
Find the x-intercept(s).
x2-25
x = 5; x = -5
Find the x-intercept(s) of this equation: 0 = x2-84
Be sure your answer is in its simplest form!
x = +2√21
x = -2√21
What is special about the patterns (in tables) of quadratic functions?
The second differences are the same.
What do we call the zeros of a quadratic function?
x-intercepts
Factor this expression: x2+3x+4 = 14
Then find the x-intercept(s).
(x+5)(x-2) = 0
x = -5; x = 2
Simplify this expression: 0 = x(x-6)
Find the x-intercept(s).
x2-6x
x = 0; x = 6
Find the x-intercept(s) of this equation: 0 = x2-364
Be sure your answer is in its simplest form!
x = +2√91
x = -2√91
Is the graph of this equation concave up or concave down? f(x)=(x+2)(x-1) How do you know?
Concave up, because in x2+x-2, the x2 is positive.
The axis of symmetry always goes through which axis?
The x-axis
Factor this expression: x2+x = -1
Then find the x-intercept(s).
Not factorable! No solutions, does not cross the x-axis.
Simplify this expression: 0 = (x-3)2
Find the x-intercept(s).
x2-6x+9
Only one, x = 3
Find the x-intercept(s) of this equation: 0 = x2+16
Be sure your answer is in its simplest form!
No real solutions, 0 x-intercepts, can't take the square root of a negative number (for now)
True or False: When a quadratic equation is graphed, it can be on its side? Explain your answer.
False: Not a function, does not pass the vertical line test.