Parent Functions in Graphing Form
What is the graphing form of a cubic function?
f(x)= a(x-h)3+k
How do h and k affect a graph?
h shifts a graph horizontally; k shifts a graph vertically
A dog jumps over a creek to retrieve a ball. If we were to assign a quadratic equation to model his path, would it have a positive or negative a value? How do you know?
negative; he starts at ground level, jumps up, then returns to ground level, so the parabola that represents his path would open down
What is an even function symmetric about (around)? Give an example of an even function.
the y-axis; f(x)=x2
What is standard form of a quadratic?
Ax2+Bx+C
What is the parent function and vertex of the following equation?
What does a determine in a quadratic equation?
Whether the graph opens up or down and vertical stretches or shrinks
What are the steps to find the vertex when modeling a real world scenario?
1. Draw a picture
2. To find the x-coordinate: 1/2 of the horizontal distance traveled
3. To find the y-coordinate: highest point vertically
What is an odd function symmetric about? Give an example of an odd function.
the origin (or x and y axes); f(x) = x3
What is graphing form of a quadratic?
f(x)=a(x-h)2+k
What is the graphing form of a rational function?
f(x)=a/(x-h) + k
Why does adding a number to x (inside parentheses) move the graph left?
Adding a number to x means we have to make x a smaller (less positive/more negative) number to balance the addition
Come up with a scenario to match the equation below.
f(x)=(x-10)2+25
answers may vary; a flea jumped 20 cm from one dog to another reaching a max height of 25 cm
What is the algebraic process of determining if a function is even or odd?
f(-x)=f(x) -> even
f(-x)=-f(x) -> odd
What is the end goal when completing the square?
To turn a quadratic in standard form into graphing form
Describe the transformations that have been applied to the function below. Include amount of change and direction.
f(x) = 4(√x+5) - 3
Vertical stretch by 4
Shift left 5 units and down 3 units
What is the multiplier and vertex of the following equation? Is it a stretch or compression?
f(x) = 2(x + 4)2 - 7
Multiplier: stretch of 2
Vertex: (-4, -7)
A snowboarder travels down a halfpipe that is 18 feet deep (below ground level) and 30 feet across. Derive an equation to measure her path from one side of the halfpipe to the other.
f(x)=6/75(x-15)2-18
Determine if the following function is even, odd, or neither.
f(x)=2x4+5x2-19
even
Complete the square:
f(x)=x2+6x+13
f(x)=(x+3)2+4
What is the multiplier and locator point (vertex) of this equation?
f(x) = 1/2 (4x+5) - 3
multiplier: 1/2
vertex: (-5, -3)
Find the vertex of the following equation:
f(x) = x2-2x-15
1. Factor: (x-5)(x+3) -> x=5, -3
2. Find midpoint: (5 + (-3))/2 = 2/2 = 1
3. Substitute x=1 into equation: 12-2(1)-15=-16
4. Vertex = (1, -16)
A quarterback throws the ball 20 yards down the field to his receiver, reaching a high point of 55 feet above the players. Derive an equation to represent the ball's path.
f(x)=-11/180(x-30)2+55
Determine if the following function is even, odd, or neither.
f(x)= 3x3+2x2-4
Complete the square:
f(x)=2x2+16x-10