Vertex Form
What is the axis of symmetry for this equation?
y=-3(x-4)^2+2
x = 4
What is the vertex of the parabola?
y=x^2-4x+1
Vertex: (2, -3)
What is the parent quadratic function?
y=x^2
Factoring the following quadratic expression.
x^2+13x+42
(x+6)(x+7)
What are the two zeros that come from the following binomials?
x(2x-3)=0
x=0, 3/2
What is the vertex of the following quadratic function?
y=(x+2)^2-7
Vertex: (-2, -7)
What is the vertex of the parabola?
y=3x^2+18x+32
Vertex: (-3, 5)
What is the following form of the quadratic function called?
y=a(x-h)^2+k
Vertex Form
Factoring the following quadratic expression.
-x^2+16x-55
-(x-5)(x-11)
What are the two zeros that come from the following binomials?
(x-3)(2x+5)=0
x=3, -5/2
If the vertex is (4, -5), what is the Axis of Symmetry?
Axis of Symmetry:
x=4
Write the quadratic function in vertex form.
y=(x-4)^2+3
y=x^2-8x+19
What is the Standard Form of the quadratic function?
y=ax^2+bx+c
Factoring the following quadratic expression.
-9x^2+6x
-3x(3x-2)
Solve the quadratic equation by factoring.
x^2-2x-24=0
x=-4, 6
Does the following quadratic function have a maximum or minimum? What is that max or min value?
y=-3(x+2)^2-4
Maximum Value of -4
Write the quadratic function in vertex form.
y=-2(x+1)^2+8
y=-2x^2-4x+6
What task is easier to complete if you have the quadratic function in Vertex Form versus Standard Form?
Graphing the Function
or find the vertex
Factoring the following quadratic expression.
3x^2+8x-3
(3x-1)(x+3)
Solve the quadratic equation by factoring.
4x^2+6x=0
x=0, -3
Does the following quadratic function have a maximum or minimum? What is that max or min value?
y=1/2x^2+3
Minimun Value of 3
What is the y-intercept of the quadratic function?
y=2x^2+4x-4
Y-Intercept: (0, -4)
What is the graph (shape of the graph) of a quadratic function called?
Parabola
Factoring the following quadratic expression.
16x^2-40x+25
(4x-5)^2
Solve the quadratic equation by factoring.
3x^2=x+4
x=-1, 4/3
Write the equation of a parabola with the given vertex and point located on the parabola in vertex form.
Vertex: (-3, 7)
a = -12
y=-12(x+3)^2+7
Does the following parabola have a maximum or minimum value?
y=-2x^2-8x+3
Maximum Value
How many possible outcomes are there when you graph a line and a parabola in the coordinate plane. Describe or sketch.
Three
1. line passes through parabola twice
2. line is horizontal and either above or below --never crosses
3. line is tangent to the parabola at 1 point
Factoring the following quadratic expression.
25x^2-9
(5x+3)(5x-3)
Using Desmos, solve the quadratic equation by graphing. Round to two decimal places.
5x^2+7x=6
x=-2, 0.6