Standard Form
The easiest key feature to find from a function in standard form
What is the y-intercept?
The easiest key feature to find from a function in factored form
What are the x-intercepts?
The easiest key feature to find from a function written in vertex form
What is the vertex?
OR
What is the axis of symmetry?
Solve the quadratic by factoring.
x2+2x=-4x-8
x=-2
x=-4
What is the concavity of the graph of y=-2x2+4x-5?
Concave Down
Find the y-intercept of y=33x2+53x-82
(0,-82)
Find the x-intercepts of the graph of y=(x-5)(x+4)
(5,0) and (-4,0)
Find the vertex of the function y=9(x-4)2-3
(4, -3)
Solve the quadratic by factoring.
x2+6x-3=9x-5
x=2
x=1
If you are given the vertex, you also immediately know this key feature
What is the axis of symmetry?
The equation for the axis of symmetry of a function in standard form
x=-b/(2a)
The equation for the axis of symmetry of a function in factored form
x=(p+q)/2
Find the axis of symmetry of the function y=-(x+5)2+3
x=-5
Solve the quadratic by factoring.
5x2+18x-2=6
x=2/5
x=-4
Three synonyms for x-intercepts
Find the axis of symmetry of y=3x2+12x-7
x=-2
Find the axis of symmetry of y=7(x+4)(x+8)
X=-6
Find the y-intercept of y=-3(x+8)2-1
(0,-193)
Solve the quadratic by factoring.
3x2+17x-10=3x-5
x=1/3
x=-5
How you find the y-intercept of a function written in ANY form
Plug in 0 for x
Find the vertex of y=x2+8x-6
(-4, -22)
Find the y-intercept of y=-5(x-2)(x+6)
(0,60)
Find the equation of the quadratic function that is reflected over the x-axis, has a vertical stretch by a factor of 8, left 9, up 4
y=-8(x+9)2+4
Solve the quadratic by factoring.
x2+3x-68=3x-4
x=-8
x=8
Identify the transformations of the function y=(-1/3)(x-5)2+2
Reflected over the x-axis, vertically compressed by a factor of 1/3, right 5 units, up 2 units