Vocab
What does leading coefficient tell us
It tells us the direction of the graph.
what are the x intercepts of this equation
y = (x + 1)(x − 10)
-1,0 and 10,0
what type of transformation is this
(hk formula)
y = x^2 + 6
up 7 h=0, k=6
Write the intercept form of
f(x) = −x^2 − 2x + 15
y=-1(x+5)(x-3)
Describe how to determine when an equation represents a linear function
The x has a power of one
Define the interval of decrease
Interval (x-value to x-value) where the function's slope is negative. The function decreases as you move from left to right.
what are the x intercepts of this equation
y = 2(3x + 8)(x − 2)
-8/3,0 and 2,0
make a description of all transformations for this function
f(x) = 2(x − 6)^3
1. dilation: narrower by factor of 3
2. translated right 6
Write the vertex form of
f(x) =1/2x^2 + 2x
y= 1/2(x+2)^2-2
Solve the quadratic equation: x^2+5x-6=0
The solutiins are x=1 x=-6
Define Range
The resulting y-values we get after substituting all the possible x-values.
what are the x intercepts of this problem
y = 2(x − 4)(x − 2)
4,0 and 2,0
The function f(x) = −(x + 3)^2 + 1 has been shifted left 3 units and up 4 units. What is the equation of the new function in vertex form?
f(x)= -(x+4)^2+7
write the intercept form of
f(x) = −x^2 − 3x + 15
y=-1(x+5)(x-3)
Solve the quadratic inequality: x²-3x+2 > 0
The solution is x<1 or x>2
Define the axis of symmetry
the vertical line going through the x-coordinate of the vertex
what are the x intercepts of this equation
y = −(x + 5)(x − 4)
-5,0 and 4,0
Consider the quadratic function f(x) = x^2. Describe the transformations that occur when the following changes are made.
The function is shifted 3 units to the right
The function becomes f(x) = (x-3)^2 The graph shifts 3 units to the right
Write the standard for of the quadratic function given the vertex form: f(x) = 3(x-2)²+5
A ball is thrown into the air with an initial velocity of 20 m/s. The height of the ball in meters after t seconds is given by the function h(t) = -5t^2+20t+10. Find the maximum height reached by the ball
The maximum height reached by the ball is 35 meters
Define domain
The set of all possible x-values which will make the function "work", and will output real y-values.
**Left to right, the x-value where the graph starts to the x-value where the graph ends, look on the x-axis
what are the x intercepts of this equation
y = 2(x − 9)(x − 1)
9,0 and 1,0
what type of transformation is this
y = (x – 8)^2
right 8
h=8
k=0
Rewrite the quadratic function in factored form: F(x) = 2x^2-5x-3
f(x)=(2x+1)(x-3)
A pistol is accidentally discharged vertically upward from a height of 2 feet above the ground. The bullet has an initial velocity of 400 feet per second.
Build the vertical motion equation that fits this scenario.
h(t) = -16t^2+400t+2