Quadratic Graphs
What is the name of the line that divides a quadratic function exactly in half?
The axis (or line) of symmetry
The "c" value in standard form tells you which charateristic of the graph?
y-intercept
The coordinates of the y-intercept for the quadratic function:
y=-2x2 + 5x - 7
What is (0,-7)?
What is the difference between domain and range?
Domain accounts for the x-values of the function and range accounts for the y-values of the function
The y component of the vertex can be found by plugging the _______ back into the original quadratic equation.
Axis of symmetry (x)
What is the name of the point on a quadratic function that will be the maximum or minimum of the function?
The vertex
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 = x2 - 8x - 20
x = 10 and x = -2
The vertex for this quadratic function:
y = x2 - 8x - 3
What is (4, -19)?
What is the y-intercept for the quadratic function?:
y=-2x2 + 5x - 7
(0,-7)
What are 3 key features of the quadratic parent function?
Answers may vary:
-domain: all real numbers
-range: y is greater than or equal to 0
-parabola opens up
-vertex is at (0,0)
-AOS is x=0
-vertex is a minimum
-when x<0, f(x) decreases; when x>0, f(x) increases
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 is the axis of symmetry for the function y= x2 + 12x +32?
x=-6
Find the coordinates of the y-intercept for the quadratic function:
y=3x2 + 2x - 1
Y-intercept (0, -1)
How does the value of a in the function affect its graph when compared to the graph of the quadratic parent function?
g(x)=-5x2
more narrow and reflection over x-axis
What is the standard form of a quadratic equation?
y = ax2 + bx + c
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)
Find the y-intercept and vertex for this quadratic function (as a decimal).
y = -5x2 +16x + 1
The y-intercept (0, 1) and
the vertex (1.6, 13.8)
Evaluate this function with f(7):
f(x) = -x2 + 3x
f(7) = -28
What is the vertex form of a quadratic equation? What are the coordinates of the vertex?
y = a(x - h)2 + k and the vertex is (h,k)\
How would I write y = x2 to shift it two spaces to the left?
y = (x-2)2
The coordinates of the vertex for this quadratic function:
y = x2 - 4x + 8
What is (2, 4)?
A function of the form g(x)=ax2 increases over the interval x<0 and decreases over the interval x>0. What is a possible value for a?
f(x) has a greater maximum value. The value is 5.