Graphing Quadratics Day 3

Graphing Quadratics

Open Ended

Question of the Day:

If you were reincarnated as an animal, what would it be and why?

Definition:

A quadratic equation forms a parabola, a "U" shaped graph.

In standard form, a quadatric is of the form y= Ax² + Bx + C

Maximum

Has a "High" point (upside down "u")

If "A" is positive the shape will be a "U" and there will be a minimum.

If "A" is negative the shape will be a "⋂" and there will be a maximum.

Vertex

intercepts

X intercepts where the graph intersects the x - axis

Y intercept is always at (0, C)
If your equation is not in Standard form (C is in the equation) you can find it by replacing "x" with "0" and solving

Match

Match the following

• Parent Function of a Quadratic

• Standard Form of a Quadratic

• Vertex Form of a Quadratic

f(x) = x²

f(x) = ax² + bx + c

f(x) = a(x - h)² + k

• f(x) = x²

• f(x) = ax² + bx + c

• f(x) = a(x - h)² + k

Fill in the Blanks

At what x value is the graph symmetrical? Type in a number based off the graph. x = ?

Fill in the Blanks

What is the low point of this quadratic? Write your answer as a coordinate (x, y).

Multiple Select

What are the x - intercepts of the quadratic shown? (Select all the apply)

• (2, 0)

• (0, 2)

• (0, 6)

• (6, 0)

Multiple Choice

Which letter determines if a parabola opens up or down?

• a

• h

• k

Multiple Choice

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

• y = -2
• x = 3
• x = -3
• y = 2

Multiple Choice

What is the "formula" for finding the axis of symmetry? 

• $$y=ax^2+bx+c$$  

• $$x=\frac{-b}{2a}$$  

• $$y=mx+b$$  

• $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$  

Drag and Drop

Given f(x)=4x²+6x-3, A is ​

Placeholder

, B is ​

Placeholder

, and C is ​

Placeholder

Drag these tiles and drop them in the correct blank above

4

6

-3

3

-4

-6

x^2

Multiple Choice

Given f(x)=3x²+6x-3, what is the y-intercept coordinate?

• (0,3)

• (-3,0)

• (0,-3)

• -3

Multiple Choice

Given f(x)=3x²+6x-3, find the axis of symmetry (x of the vertex, x_v) using x=-B/2A

• 1

• -1

• 1.5

• -1.5

Multiple Choice

Given f(x)=3x²+6x-3, having found x_v=-1 find y_v

Using f(-1)=3(-1)²+6(-1)-3

• -6

• 6

• -9

• 9

Multiple Choice

What is a, b, and c in 3x² + 4 = 5x? (Hint put into Standard Form First)

• a = 3, b = -5, c = 4
• a = 3, b = 5, c = 4
• a = 3, b = 5, c = -4
• a = 3, b = -5, c = -4

Multiple Choice

Find the axis of symmetry for
f(x) = x²- 8x + 15.

• x = -4
• x = 4
• y = 4
• y = -4

Open Ended

Brain Break:

What is the best holiday food?

Multiple Choice

• a. (-6, 1)

• b. (6, 1)

• c. (-6, -1)

• d. (6, -1)

Multiple Choice

If given the equation
y = 3(x + 5)² - 4,
what is the vertex of the parabola?

• (5, -4)
• (-5, -4)
• (-15, -4)
• (15, -4)

Multiple Choice

What is the equation of this graph?

• f(x) = (x -5)² + 1
• f(x) = (x - 1)² - 5
• f(x) = (x + 1)² - 5
• f(x) = (x + 5)² +1

Multiple Choice

According to the graph, what was the highest elevation reached?

• 1.75 seconds

• 3.53 seconds

• 15.51 meters

• 12.75 meters

Multiple Choice

According to the graph, how long was the projectile in the air?

• 1.75 seconds

• 3.53 seconds

• 12.75 seconds

• 15.51seconds

Multiple Choice

What was the initial elevation (original height) of the projectile?

• 0

• 128

• 144

• 4

Multiple Choice

When was the projectile 128 units up in the air?

• It never reached that height

• after 1 unit of time

• after 2 units of time

• after 0 and 2 units of time