Quadratic Graphs
What is the value 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)?
What number goes in the blank for the next step in completing the square?
x² – 12x + ____ = – 22 + ____
36
The y component of the vertex can be found by plugging the _______ back into the original quadratic equation.
Axis of symmetry (x)
What determines whether a function will have a maximum turning point or a minimum turning point?
Whether or not the a-value is negative.
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
The vertex for this quadratic function:
y = 5(x-2)(x-6)
(4,-20)
Find the equation of a quadratic in vertex form through that has a vertex of (-2,6) and is opens down.
y= -(x+2)2 + 6
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
Find the y-intercept and vertex for this quadratic function (round to nearest tenth).
y = -4.9x2 +16.4x + 1
The y-intercept (0, 1) and
the vertex (1.7, 14.7)
What are the solutions to the equation x2-3x−7=0?
x=(3 ± √37) / 2
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)
Find the domain of the function:
y= -2x2 + 8x + 7
Domain: All real #s
What equation reveals the minimum value of the function f(x)=x2−6x+1?
(x−3)2−8
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)
On what intervals does the following function increase?
y= 1/4x2 - 3x+2
Increasing: (6, Infinity) x > 6
Analyze the data to determine whether it models a quadratic relationship. If so, explain why.
(1,36), (2,60), (3,84), (4, 108)
Yes because the second difference is constant