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
Solve the quadratic equation below:
y = (x - 4) (x + 5)
x = 4 and -5
Solve the quadratic equation be:
y = 3x2 + 3x - 6
(0, -6)
Find the vertex of f(x) = -(x - 3)2+ 8
(3,8)
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
Solve the quadratic equation below:
y = x (x - 6)
x = 0 and 6
What direction will the parabola open?
y = -3x2 -7x + 8
Down
Find the vertex of f(x) = -x2 - 9
(0, -9)
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 found using the h value of a quadratic equation in vertex form.
x-coordinate
What does FOIL stand for when changing an equation in factored form to standard form?
First, Outer, Inner, Last
What is the general formula for a quadratic equation in standard form?
y = ax2 + bx + c
Find the vertex of f(x) = -(x + 2)2
(-2, 0)
This line crosses the vertex of a parabola and divides the parabola in half
axis of symmetry
Quadratic equations in factored form can be converted to standard form by applying the ____________ property.
Distributive
Convert the standard form equation below to factored form:
y = x2 + 8x + 12
y = (x + 2) (x + 6)
What is the vertex of:
y= -x2 + 2
(0, 2)
Write a quadratic equation in vertex form that has a vertex of (-3, 4) and faces down.
Answers will vary.
Example:
y = - (x + 3)2 + 4
This function is the simplest form of a quadratic function
Parent function
The opposite of applying the distributive property is called _____________.
Factoring
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:
f(x) = -(x + 2)2
f(x) = -x2 - 4x - 4
Write a quadratic equation in vertex form that has a vertex of (2, 0) and faces up.
Answers will vary.
Example:
y = - (x - 2)2