VOCABULARY
This is the variable representing the axis of symmetry in vertex form, y = a (x - h)^2 + k
What is h?
This is how you go from the axis of symmetry to the y-value of the vertex for standard or factored form.
How do you plug in the x-value of x = h into the equation, replacing all of the x with the x-value?
These are what the three forms of quadratics are called.
Vertex Form, Standard Form, Factored/Intercept Form
This is what the graph of a parabola looks like when a is less than zero.
What is: it opens downward like a sad face?
y = 4x^2 + 7 has its vertex at this point.
What is (0,7)?
This is y = (x + 1)^2 - 3 in standard form.
What is y = x^2 + 2x - 2?
This is the end behavior of any parabola that opens up.
Up and up (would be down and down for a parabola opening down, like a frowny face).
The vertex of y = (x - 1)^2 is this ordered pair.
What is (1,0)?
This is y = 2 (x - 3) (x + 1) in standard form.
What is y = 2x^2 - 4x - 6?
What happens when |a|>1 (a gets bigger and farther away from zero, ex. 2, -4)?
Stretches (tall & skinny)
These are names for the place or places a parabola crosses the x-axis.
What are x-intercepts, roots and zeros?
This is the formula for the axis of symmetry from standard form, y = ax^2 + bx + c.
What is x = -b/2a ?
This is y = x2 -4x +5 in vertex form.
What is y = (x-2)2 + 1?
What happens to the graph when h = 2 and k = -3 ?
Shifts right 2 units (for h) and down 3 units (for k)
This is the formula for axis of symmetry from factored form, y = a (x - r) (x - s).
This is x = 1/2 (r + s).
The vertex of y = -2(x - 1)(x + 3) is this.
What is (-1, 8)?
Create an example of each form of quadratic and label each.
(Answers may vary)
This is how you make a table to graph a quadratic.
You find the vertex, put that x-value and y-value into the middle row of a x/y table, and plug in the x-values of two points to the left and to the right to end up with five total points.