HPC Section 2.1 Part 1

HPC Section 2.1

Quadratic Functions

Multiple Choice

What is the vertex of the parabola?

$$f\left(x\right)\ =\ -x^2$$  

• (0, 0)

• (1, 0)

• (1, 1)

• (0, 2)

Multiple Choice

What is the vertex of the parabola?

$$f\left(x\right)\ =\ x^2-3$$  

• (0, 0)

• (3, 0)

• (0, -3)

• (-3, 0)

• (0, 3)

Multiple Choice

What is the vertex of the parabola?

$$f\left(x\right)\ =\ \left(x-4\right)^2$$  

• (0, 0)

• (4, 0)

• (0, -4)

• (-4, 0)

• (0, 4)

Multiple Choice

What is the vertex of the parabola?

$$f\left(x\right)\ =\ \left(x+1\right)^2+2$$  

• (0, 0)

• (1, -2)

• (-1, -2)

• (-1, 2)

• (1, 2)

Multiple Choice

What is the vertex of the parabola?

$$f\left(x\right)\ =\ x^2+2x+3$$  

• (0, 0)

• (1, -2)

• (-1, -2)

• (-1, 2)

• (1, 2)

Polynomials

What do you remember?

Multiple Choice

What is the leading coefficient of the following polynomial?
5x² - 3x + 6

• 2
• -3
• 5
• 6

Multiple Choice

Which is an example of a linear polynomial?

• x² - 5

• 6x + 4

• 5x⁵
• 2x³ - 9x²

Multiple Choice

Find the constant in the polynomial:

x⁴ - 7x³ + 3x² - 2x + 5

• 1

• 2

• 5

• 0

Multiple Choice

Which is an example of a cubic binomial?

• x³ + 5

• x² + 3

• x² + 5x - 6

• 5x³

Multiple Choice

Classify the polynomial by its degree.
x² + 2x³ - 4

• A
  binomial
• B
  trinomial
• C
  quadratic
• D
  cubic

Multiple Choice

Which of the following is a 5th degree trinomial with a leading coefficient of -2? 

• -2x⁵ + 3x - 1
• 5x^-2 +3x - 2

• -2x⁵ + 3x⁴ + 2x³ + x² - 10
• -2x + 5

Multiple Choice

Determine the "degree" of this polynomial?

$$f\left(x\right)=x^3+6x-2x^4+7x^5+12$$

• 1

• 3

• 4

• 5

• 12

Multiple Choice

How do you determine the "degree" of a polynomial?

$$f\left(x\right)=x^3+6x-2x^4+7x^5+12$$

• It is the leading coefficient.

• It is the exponent of the first term

• It is the exponent of the highest power in the polynomial

• It determines the optimal temperature of the polynomial

Open Ended

Partner up. In a group of 2 or 3 discuss the following graph and then designate one person to type a agreed upon description of the graph for the group. Include the vertex of the parabola in your description.

$$f\left(x\right)\ =2x^2+1$$  

Open Ended

Partner up. In a group of 2 or 3 discuss the following graph and then designate one person to type a agreed upon description of the graph for the group. Include the vertex of the parabola and the axis of symmetry in your description.

$$f\left(x\right)\ =\left(x+3\right)^2-4$$  

Open Ended

Partner up. In a group of 2 or 3 discuss the following graph and then designate one person to type a agreed upon description of the graph for the group. Include the vertex of the parabola and the axis of symmetry in your description.

$$f\left(x\right)\ =x^2-4x+4$$  

​Find the vertex

​Find the vertex

Open Ended

Your turn:  Find the vertex of the parabola.

$$f\left(x\right)\ =\ x^2-4x+9$$  

1 - 3, 5 - 9, 11 - 23 odd, 27, 29

​on 23, 27 and 29 factor or complete the square to get the equation into standard form to find the vertex.

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