Vocabulary
What is the name for a U-shaped graph in the quadratic equation?
Parabola
What is the y-intercept and its general form?
Point where the parabola crosses through the y-axis. The form is (0, c).
Name the x-intercepts. Give the points where the parabola is crossing the x-axis: y = (x-2)(x+6)
(2,0) and (-6,0)
What is the formula for the axis of symmetry?
x = -b/2a
What is the first step when solving for x-interepts and the coefficient for "a" is negative? y = ax^2 + bx + c
Divide out/factor by -1 or the negative coefficient
What do we call the highest or lowest point on a parabola?
Vertex
What is this form called? a^ - b^2 = (a+b)(a-b)
Difference of Squares
Name the x-intercepts. Give the points where the parabola is crossing the x-axis: y = (x)(x-2)
(0,0) and (2,0)
What does the axis of symmetry do?
Axis of symmetry cuts the quadratic equation in half.
Use factoring to solve the quadratic equation: m^2 - m = 0
m = 0 and m = 1
What is the name of the form for this quadratic equation? y = ax^2 + bx + c
Standard form
What can the sign of the coefficient of an "a" term tell you about the behavior of the parabola? y = ax^2 + bx + c
The "a" term tells you whether the parabola is facing upward or downward.
Name the x-intercepts. Give the points where the parabola is crossing the x-axis: y = x^2 - 4
(-2,0) and (2,0)
What is the axis of symmetry for this quadratic function? y = x^2 + 4x + 4
x = -2
Use factoring to solve the quadratic equation: m^2 + 3m - 40 = 0
x = 5 and x = -8
Find the vertex of the following quadratic equation: y = x^2 + 2x + 3
(-1, 2)
Name the x-intercepts. Use factoring to find the points where the parabola crosses through the x-axis: y = x^2 - x - 2
(-1,0) and (2,0)
What is the axis of symmetry for this quadratic function? y = x^2 - 6x + 9
x = 3
Use factoring to solve the quadratic equation: x^2 - 25 = 0
x = -5 and x = 5
What do we call the line that runs through the vertex and divides the parabola in half?
Axis of symmetry
Name at least 3 steps that you need to take to graph the quadratic function.
(1) Find the axis of symmetry (Find x). (2) Find the value of y. (3) Find vertex (x,y). (4) Plot the vertex. (5) Find the x-intercepts. (6) Find the y-intercept. (7) Plot axis of symmetry. (8) Use axis of symmetry to plot remaining points.
Name the x-intercepts. y = x^2 - 10x + 21
(7,0) and (3,0)
What is the axis of symmetry for this quadratic function? x^2 + 1 = 2x
x = 1
Use factoring to solve the quadratic equation: 4a^2 + 16a - 20 = 0
a = 1 and a = -5