Quadratic Graphs
How many zeros (x-intercepts) can a quadratic function have?
What is 2, 1, or none?
The value of "a" for a graph of a quadratic function opening downward.
What is negative?
The coordinates of the y-intercept for the quadratic function:
y=-2x2 + 5x - 7
What is (0,-7)?
If the x-intercepts of a function are x = 6 and x=12, what is the Axis of Symmetry (x-value of the vertex)?
x = 9
*Mrs. Reid will show you the information (S1)
Yes - it passes the vertical line test
The shape of the graph of a quadratic function.
What is a parabola?
The vertex of the quadratic function y = 5x2 + 10x - 2 is a ____________________ point.
What is minimum?
Find the zeros (x-intercepts) of the following:
y = x2 - 8x - 20
x = 10 and x = -2
The vertex for this quadratic function:
y = x2 - 8x - 3
Is this a function? How do you know?
*Mrs. Reid will show you the picture (S12)*
No - it does not passes the vertical line test
The name of the line that divides a quadratic function exactly in half.
What is the axis of symmetry?
Order the following quadratic functions from narrowest to widest:
y=4x2 y=-12x2 y=11x2 y=-2x2
What is y=-12x2, y=11x2, y=4x2, y=-2x2?
What determines whether a function will have a maximum turning point or a minimum turning point?
Whether or not the highest power term is negative.
The coordinates of the y-intercept and x-intercepts for the quadratic function:
y=3x2 + 2x - 1
What is y-intercept (0, -1) and x-intercepts (-1, 0) (0.33, 0)?
Evaluate this function with f(-5):
f(x) = 2x3 + 15x
f(-5) = -325
The name of the point on a quadratic function that will be the maximum or minimum of the function.
What is the vertex?
Order the following quadratic functions from widest to narrowest:
y=4x2 y=2/3 x2 y=-2x2 y= x2
What is y=2/3 x2, y= x2, y=-2x2, y=4x2
Find the vertex for the quadratic function:
y = x2 + 10x + 6
What is (-5, -19)
The y-intercept, x-intercepts, and vertex for this quadratic function:
y = -4.9x2 +16.4x + 1
What is the y-intercept (0, 1), the x-intercepts (-0.06, 0) (3.4, 0) and the vertex (1.7, 14.7)?
Evaluate this function with f(7):
f(x) = -x2 + 3x
f(7) = -28
The domain of a quadratic function
What is xER?
For : y = x2 - 6x + 5
a) state the x-intercepts
b) state the vertex
x = 5 and x = 1
Vertex (3, -4)
The coordinates of the vertex for this quadratic function:
y = x2 - 4x + 8
What is (2, 4)?
The transformation chart for:
y = -5x2 +10x + 2
Vertex: (1, 7)
A of S: h = 1
Stretched by 5
opens down
Domain: {xER}
Range: {yER|y<7}
x-intercepts: (-0.18, 0) (2.18, 0)
y-intercept: (0, 2)
How do you know if a table of values is a function or not?
If each input (x-value) has only one output (y-value), then it is a function