Simplifying & Solving
Simplify:
4x(2x-3)+5x
8x²-7x
Solve for b:
a=b+c
Answer: b=a-c
Factor:
x²+9x+20
(x+5)(x+4)
A basketball shot reaches its highest point halfway through the shot.
What key feature represents the highest point?
Vertex
What do we call a math sentence that has an equals sign?
Equation
Simplify:
-6y(2y+1)+4y(y-5)
-8y²-26y
Solve for x:
y=3x+8
x=(y-8)/3
Factor:
x²-16
(x-4)(x+4)
A fireworks display rises into the air and then falls back down.
Does the parabola have a maximum or minimum value?
Maximum
What do we call a math phrase with numbers, variables, and operations but no equals sign?
Expression
Solve:
(2x+6)/4 = 5
x = 7
Solve for t:
d=rt
Answer: t=d/r
Solve using factoring:
x²-7x+12=0
Answer: x=3 and x=4
A skateboard ramp is shaped like a parabola opening upward.
What key feature represents the lowest point of the ramp?
Minimum
What do we call a polynomial with a highest exponent of 2?
Quadratic
Solve:
7x-9 = 4x+18
x = 9
Solve for r:
A=πr²
Answer: r=√(A/π)
Solve using the quadratic formula:
x²+2x-8=0
Answer: x=2 and x=-4
A football is kicked and follows a parabolic path. What is The point where the ball is evenly balanced on both sides of the path / the midpoint of the flight?
Axis of Symmetry
What is the name of the number in front of a variable?
Example: In 7x, the number 7 is called this.
Coefficient
Solve:
3(x-4)=2x+11
x = 23
Solve for m:
P=2l+2m
Answer: m=(P-2l)/2
The function y=-2x²+16x-5 models a parabola. What is the x-value of the vertex?
Answer: x=4
The Quadratic is shown:
y=-3x²+36x+200
What is the x-value of the vertex?
6
What do we call the set of all possible input values of a function?
Domain