Features of Parabolas
This is the point where a quadratic function crosses the y-axis
y-intercept
The ___________ form of quadratic equations is useful for identifying the y-intercept.
Standard
Give the x-intercepts for the function:
y = (x - 4) (x + 5)
(4,0) and (-5,0)
Give the y-intercept for this quadratic function written in standard form:
y = 3x2 + 3x - 6
(0, -6)
What is the difference between the graph of y=x2 and the graph of y=x2+5? Be specific.
Moved up 5 units.
These are the points where a quadratic function crosses the x-axis
x-intercepts
The __________ form of quadratic equations is useful for finding the x-intercepts.
Factored
Give the x-intercepts for this quadratic function:
y = x (x - 6)
(0,0) and (6,0)
What direction will the parabola open?
y = -3x2 -7x + 8
Down
What is the difference between the graph of y=x2 and the graph of y=-x2? Be specific.
Parabola is flipped.
This point is the center of a parabola and can be a maximum or minimum, depending on the direction of the parabola.
Vertex
The _____________ of the vertex is the midpoint between the two x-intercepts.
x-coordinate
Convert the factored form equation below to standard form by distributing:
y = (x + 2) (x + 6)
y = x2 + 8x + 12
What is the general formula for a quadratic equation in standard form?
y = ax2 + bx + c
What is the difference between the graph of y=x2 and the graph of y=4x2-8? Be specific.
Parabola is steeper/skinnier and is moved down 8 units.
x-coordinate of the vertex
Quadratic equations in factored form can be converted to standard form by applying the ____________ property.
Distributive
Write a quadratic equation in factored form that will have the following x-intercepts:
(-2, 0) and (4, 0)
Answers may vary.
Example:
y = (x + 2) (x - 4)
Rewrite the function below in standard form by distributing:
f(x) = (x + 2)2
f(x) = x2 +4x + 4
What is the difference between the graph of y=x2 and the graph of y=0.25x2+2? Be specific.
Parabola is less steep/wider and moved up two units.