Graphing Parabolas

Finite Math

7.3a Graphing Quadratic Functions

EQ’s for Friday, October 13, 2023

● How do I graph a Quadratic Function?
● How do I find part of a parabola?

Ways to Graph a Quadratic Function (Parabola)

● Plotting Points
● Using Vertex Form
● Using Standard Form

Parts of a Parabola

●

Vertex (max or min)

●

Axis of symmetry (line that goes
through vertex)

●

x-intercepts (0, 1, or 2)

●

y-intercept (only 1)

Multiple Choice

The Vertex is a

• Maximum, because it is the high point on the graph.

• Minimum, because it is the parabola opens down.

Multiple Choice

The axis of symmetry is

• x = 2

• y = 9

• 2

• undefined

Math Response

$$f\left(x\right)=2x^2-3x+5$$

Evaluate the Quadratic Function for

$$f\left(-3\right)$$

Type answer here

Correct Answer: 32

Deg^°

Rad

Graphing a Quadratic Function by Plotting Points

x

(x,y)

-5

-4

-3

-2

-1

0

1

Graphing a Quadratic Function by Plotting Points

(x,y)

(-5, 8)

(-4, 3)

(-3, 0)

(-2, -1)

(-1, 0)

(0, 3)

(1, 8)

Draw

Plot the Points of the Parabola

Graphing a Quadratic Function by Plotting Points

(x,y)

(-5, 8)

(-4, 3)

(-3, 0)

(-2, -1)

(-1, 0)

(0, 3)

(1, 8)

Quadratic Functions

● Using Vertex Form

● Using Standard Form

Quadratic Functions

● Using Vertex Form

● Using Standard Form

Quadratic Functions

● Using Vertex Form

● Using Standard Form

Quadratic Functions

● Using Vertex Form

● Using Standard Form

Quadratic Functions

● Using Vertex Form

● Using Standard Form

Multiple Choice

Which equation is in vertex form?

• y = ax^2 + bx + c
• y = mx + b
• y = a(x-h)(x-k)
• y = a(x-h)^2 + k

Multiple Choice

What is the vertex of the parabola?

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

• (2, 4)
• (3, 4)
• (3, 2)
• (-3, 4)

Multiple Choice

Give the axis of symmetry for the parabola.

$$f\left(x\right)=2\left(x+5\right)^2-1$$

• x = 2

• x = 10

• x = 0

• x = -5

• x = 5

Multiple Choice

What is the axis of symmetry for the parabola?

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

• x = 1

• x = 0

• x = 2

• x = -1

Multiple Choice

What is the vertex of the parabola?

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

• (1, -5)
• (0, -3)
• (1, 5)
• (2, -3)

Graphing a Quadratic Function from Vertex Form

1. Plot the Vertex (h, k)
2. Draw AOS (x = h)
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

1. Plot the Vertex (h, k)
2. Draw AOS (x = h)
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

Multiple Choice

Give the vertex of the parabola.

• (-4, 1)

• (-4, -1)

• (4, -1)

• (4, 1)

Multiple Choice

Give the axis of symmetry for the parabola.

$$f\left(x\right)=-\frac{1}{2}\left(x+4\right)^2-1$$

• x = -4

• x = 4

• x = -2

• x = -1

Multiple Choice

Give the point on the parabola when x = -2.

• (-2, -3)

• (-2, 1)

• (-2, -1)

• (-2, -4)

Multiple Choice

Know that the axis of symmetry is x = -4 and (-2, -3) is on the parabola, which point must also be on the parabola?

• (-4, -5)
• (-2, -5)
• (-6, -3)
• (-8, -3)

1. Plot the Vertex (h, k)
2. Draw AOS (x = h)
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

Write the equation of the parabola in Vertex form.

Write the equation of the parabola in Vertex form.

Graphing a Quadratic Function from Standard Form

1. Draw AOS (x = − b/2a)
2. Plot Vertex (x, f(x))
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

1. Draw AOS (x = − b/2a)
2. Plot Vertex (x, f(x))
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

1. Draw AOS (x = − b/2a)
2. Plot Vertex (x, f(x))
3. Get 2 points, copy to other

side of AOS

4. Sketch the graph

Finding a Parabola’s x-intercepts

Finding a Parabola’s x-intercepts

Finding a Parabola’s y-intercepts

Finding a Parabola’s y-intercepts

Finding a Parabola’s Axis of Symmetry

Finding a Parabola’s Axis of Symmetry

Finding a Parabola’s Vertex

Finding a Parabola’s Vertex