Quadratic Graphs
What is the sign of "a" for a graph of a quadratic function opening downward.
"a" is negative
The "c" value in standard form tells you which charateristic of the graph?
y-intercept
What is the y-intercept for the quadratic function?:
y=-2x2 + 5x - 7
What is (0,-7)?
Solve by Factoring
x2+2x=3
x=-3,1
x2 − 12x + 11 = 0
11, 1
x2 − 4x + 4 = 0
2
What determines whether a function will have a maximum turning point or a minimum turning point?
If a is negative or positive
Is the vertex of the quadratic function y = 5x2 + 10x - 2 a maximum or minimum point?
It's a minimum
Find the zeros (x-intercepts) of the following:
y= 3 (x-6)(x+4)
x= -4 and x= 6
Solve by Factoring
x2+16=10x
x = 2,8
x2 + 14x − 15 = 0
1, -15
x2 + 4x + 3 = 0
-1, -3
What is the name of the line that divides a quadratic function exactly in half?
The axis of symmetry
What properties does vertex form tell us about parabolas?
the vertex
Find the zeros (x-intercepts) of the following:
y = x(x-10)
x =0 and x=10
Solve by Factoring
x2-5x+6=0
x = 2, 3
x2 + 4x = 5
1, -5
What is the name of the point on a quadratic function that will be the maximum or minimum of the function?
The vertex
What properties does factored form tell us about parabolas?
zeros/ x-intercepts
Find the vertex for the quadratic function:
y = x2 + 10x + 6
(-5, -19)
Solve by Factoring
6n2 - n=2
n = -1/2, 2/3
x2 = −4 + 8x
x = 4 +- 2sqrt3
How many zeros (x-intercepts) can a quadratic function have? List all possibilities.
2, 1, or none
What properties does standard form tell us about parabolas?
direction it opens and y-intercept
What is the vertex for this quadratic function:
y = 2(x-2)2 - 3
(2, -3)
Solve by Factoring
2x2-8=31x-2x2
x = -1/4, 8
x2 - 4x + 2 = 0
2+- sqrt2