8.3 Standard form

8.3 Standard form

Mrs. Nickodemus

Multiple Choice

The standard form of a quadratic function is

• ax² + bx + c

• a(x - h)² + k

• y - y₁ = m(x - x₁)

• Ax + By = C

Multiple Choice

So, at f(0)= ax^2 + bx + c , f(0) = c.

The point with the x value 0 (x=0 or (0, ___) has a special name. What is it?

• y-intercept

• x-intercept

• minimum

• maximum

• constant

Multiple Choice

What is the axis of symmetry?

• the slope of the graph
• the dividing line for a parabola
• a way to spin my pencil
• the x-axis

Multiple Choice

What is the vertex?

• (2, 4)
• (3, -1)
• (0, 8)
• (4, 2)

Multiple Choice

What is the formula to find the axis of symmetry of a parabola?

• x = -b/2

• x = -b

• x = -b / (2a)

• x = -b / 2

Multiple Choice

Identify A, B, and C if y=3x²-8+5x

• A=3, B=5, C=-8

• A=3, B=-8, C=5

• A=3x², B=5x, C=-8

• A=3x² , B=-8, C=5x

Multiple Choice

What is c in the following equation?
y=ax²+bx+c

• Zeroes
• Axis of Symmetry
• Direction
• y-intercept

Multiple Choice

What is the vertex?
f(x) = -x² - 4x + 12.

• (-2, 16)
• (2, 0)
• (2, 4)
• (-2, 4)

Multiple Choice

What is the y-intercept?
f(x) = -2x² + 4x - 6

• (0, 6)
• (0, -6)
• (6, 0)
• (-6, 0)

Multiple Choice

What is the axis of symmetry?
f(x) = x² - 8x + 15.

• x = -4
• x = 4
• y = 4
• y = -4

Multiple Choice

Graph the quadratic.

• A
• B
• C
• D

Multiple Choice

Graph the quadratic.

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

 $y=-\frac{2}{3}(x-9)^2-2$  
Convert the equation from vertex form to standard form

•  $y=-\frac{2}{3}x^2-12x-52$  

•  $y=-\frac{2}{3}x^2+12x-56$  

•  $y=-\frac{2}{3}x^2+18x-56$  

•  $y=-\frac{2}{3}x^2-18x+52$  

Multiple Choice

 $y=4(x+2)^2-8$ 

Convert the equation from vertex form to standard form. 

•  $y=4x^2+16x+8$  

•  $y=4x^2+16x+16$  

•  $y=16x^2+64x-8$  

•  $y=16x^2+256x+8$  

Multiple Choice

 $y=-5(x+2)^2-10$  
Convert the equation from vertex form to standard form.

• y = -5x² - 20x - 30

• y = -5x² - 4x - 10

• y = 25x² + 100x + 90

• y = 25x² - 10x - 30

Multiple Choice

 $y=-3(x+5)^2-4$  
Convert the equation from vertex form to standard form.

• y = 9x² - 15x + 21

• y = -3x² - 75x - 4

• y = 9x² + 90x + 221

• y = -3x² - 30x - 79

Open Ended

How does the vertex form compare to the standard form?

Poll

Which of these two forms do you prefer?

• Vertex Form

• Standard Form

Open Ended

How are ax^2 +bx +c and ax^2 +bx similar and how are they different?

Open Ended

How do you write vertex form into standard form? (explain using your math vocabulary and English skills)

Open Ended

Why might it be useful to convert from vertex form to standard form?