Polynomial Review for RollerCoaster project

Polynomial Review for RollerCoaster project

do you see the polynomials

Vocabulary to remember

 $y=\left(2x+3\right)\left(3x-4\right)$ 
factored form

 $=6x^2-2x-12$ 
Standard form

Lines ONE

 $y\ =.1\left(x-3\right)^1$  for long straight runs the coefficient should be very small. positive for increasing, negative for decreasing.

Multiple Choice

What type of slope?

• negative

• positive

• zero slope

• downward slope

Multiple Choice

What type of slope is represented in the image?

• Positive Slope

• Negative Slope

• Zero Slope

• Undefined Slope

Multiple Choice

What type of slope is represented in the image?

• Positive Slope

• Negative Slope

• Zero Slope

• Undefined Slope

Multiple Choice

What type of slope?

• undefined

• positive slope

• negative slope

• zero slope

Quadratics/Parabolas TWO

 $y=+1\left(x+2\right)\left(x-3\right)$  the factors determine the x-intercepts  The coefficient determines if the parabola opens up or down

Notice where they intersect.

both have an x-intercept of (3,0)

Multiple Choice

What is the equation for this parabola in factored form?

• y=(x+2)(x-1)
• y=(x-2)(x+1)
• y=(x-2)(x-1)
• y=(x+2)(x+1)

Multiple Choice

Does the quadratic have a max/min vertex, and does the parabola open up/down?

• max/ opens down

• min/ opens up

• max/ opens up

• min/ opens down

Multiple Choice

Which quadratic equation models the parabola shown below?

• y = 0.25(x-2)(x+2)

• y = -0.25(x-2)(x+2)

• y = 4(x-2)(x+2)

Multiple Choice

Which quadratic equation models the parabola shown?

• y = (x-2)(x+5)

• y = (x+2)(x+5)

• y = -(x-2)(x-5)

• y = -(x+2)(x+5)

Multiple Choice

Which quadratic equation models the parabola shown?

• y = (x-2)(x-5)

• y = (x+2)(x+5)

• y = -(x+2)(x+5)

• y = -(x-2)(x-5)

Multiple Choice

This goes to the point (3,0) and then increases.

Which equation connects to this graph?

• $y=x^2$

• $y=\left(x-3\right)^2$

• $y=\left(x+3\right)^2$

• $y=\left(x-3\right)\left(x+3\right)$

Multiple Choice

This goes to the point (3,0) and then decreases.

Which equation connects to this graph?

•  $y=-x^2$ 

•  $y=-\left(x-3\right)^2$ 

•  $y=-\left(x+3\right)^2$ 

•  $y=-\left(x-3\right)\left(x+3\right)$ 

Cubics THREE

 $y=\left(x-3\right)\left(x-5\right)\left(x-10\right)$ 

There are 3 factors and each factor is connected to an x-intercept.

Multiple Choice

Identify the zeros:

• x=-2, x=-1, x=0

• x=-2, x=0

• x=-1, x=0, x=2

• x=-2, x=0, x=1

Multiple Choice

Which of the following could be the equation of the graph shown?

• f(x) = x(x+3)

• f(x)=x(x+3)²

• f(x) = x(x-3)

• f(x)=x(x-3)²

Multiple Select

f(x)=x(x+4)(x-3)

Select ALL zeros for this function.

• x = -4

• x = 4

• x = -3

• x = 3

• x = 0

Multiple Choice

How many x-intercepts does this function have?

• 1

• 2

• 3

• 4

Multiple Select

Which statements are true about  $y=2(x-3)^2(x+1)$  ?  

• 3 is a zero of the function.

• The function will cross the x-axis at x = -1.

• The function has an x-intercept at x = -3.

• The function has a degree of 3.

Quartics FOUR

 $y=\left(x-3\right)\left(x+2\right)^2\left(x-10\right)$  

Quartics have four factors, some can be repeated and that changes the look of the graph

notice the y-axis scale (4000!)

Quintics FIVE

Degree the largest exponent

Leading term the coefficient and variable with the largest exponent

zeroes are x-intercepts

Multiple Choice

What is the degree of the graphed polynomial?

• 2

• 3

• 4

• 5

Multiple Choice

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

• Degree: 6
• Degree: 5
• Degree: 3
• Degree: 2

Multiple Choice

f(x) = -3x⁴ + x³ - 2x² + x - 1

What is the y-intercept of f(x)?

• (-1, 0)

• (0, -1)

• (-3, 0)

• (0, -3)

Multiple Choice

Determine the y-intercept 
f(x) = x³ - 5x² - 25x + 125

• (0,0)
• (0,25)
• (0,125)
• (0,5)

Multiple Choice

What is the degree of (x + 2)(x - 1)(x + 3)(x - 2)²?

• 2
• 3
• 4
• 5

Multiple Choice

• Even Degree
  - Leading Coeff.
• Even Degree
  + Leading Coeff.
• Odd Degree
  - Leading Coeff.
• Odd Degree
  + Leading Coeff.