Domain & Range of Quadratic Equations

Domain & Range of Quadratic Equations

We will write the domain and range of quadratic equations in inequality notation.

Essential Question

How can you describe the graph of f(x) compared to the graph of f(x), if a is a negative number?

Let's Recap

Lets make sure we can identify the vertex, minimum, maximum, axis of symmetry and determine the domain and range.

Multiple Choice

The highest or lowest point on a quadratic is called the...

• Max

• Vertex

• Axis of Symmetry

• Intercept

Multiple Choice

The line that goes through the vertex of a parabola is called the...

• Vertex

• Axis of Symmetry

• x-intercept

• y-intercept

Multiple Choice

Determine the domain and range of the function

• Domain: All real numbers

  Range: All real numbers

• Domain: x ≥ -4

  Range: All real numbers

• Domain: All real numbers

  Range: y ≥ -4

• Domain: -1 ≤ x ≤ 5

  Range: y ≥ -4

Multiple Choice

What is the domain and the range for the graph?

• Domain : -2 ≤ x ≤ 2

  Range : 0 ≤ y ≤ 4

• Domain : 0 ≤ x ≤ 4

  Range : -2 ≤ y ≤ 2

• Domain : All real #s

  Range : y ≤ 4

• Domain : -2 ≤ x ≤ 2

  Range : y ≤ 4

Multiple Choice

Does this parabola have a minimum or maximum and what is its value?

• minimum: 2

• maximum: 2

• minimum: 5

• maximum: 5

Multiple Choice

Does the following graph have a maximum or minimum.

• Maximum

• Minimum

Multiple Choice

Quadratic equations take the shape of a _______ when graphed.

• parabola

• straight line

• snaked line

• elliptical

Domain and Range of Quadratic Equations

We will use a formula to determine the domain and range of the given equation.

Domain Quadratic Equations

This is ALWAYS the case IF and only IF the equation in in its standard form.

Range Quadratic Equations

You need to know which way it opens, and the y-coordinate of the vertex.

Range Quadratic Equations Part I

If a > 0 then the parabola opens upward

If a < 0 then the parabola opens downward

Multiple Choice

Determine the value of a. (*Remember y = ax² + bx + c)

f(x) = x² - 8x + 15.

• a = -1

• a = 1

• a = -8

• a = 15

Multiple Choice

Which way does the parabola open up?

f(x) = x² - 8x + 15.

• up

• down

Multiple Choice

Determine the value of a.

y = -2x² + 4x + 3

• a = 2

• a = 4

• a = -2

• a = 3

Multiple Choice

Which way does this parabola open?

y = -2x² + 4x + 3

• up

• down

Range of Quadratic Equations Part II

You have to find the values for b and a from the equation

y = ax² + bx + c

Multiple Choice

Determine the value of b.

y = x²+4x-21?

• 1

• 4

• 2

• -21

Multiple Choice

Solve for x.

y = x²+4x-21?

• -2

• 2

• 1

• -1

Multiple Choice

What is vertex of the quadratic function x²+4x-21?

• (4, -21)

• (-2,-25)

• (2, -21)

• (4, -25)

Multiple Choice

Find the Vertex:

y = x² + 6x + 2

• (-3,-7)

• (1,6)

• (6,2)

• No Real Solution

Multiple Choice

Find the vertex of the following quadratic equation:

y = -x² +2x + 1

• (1, 2)

• (-1, -2)

• (-1, 3)

• (0, 0)

Multiple Choice

Find the vertex of the following quadratic equation:

y = 3x²

• (0, 3)

• (-3, 0)

• (o, -3)

• (0, 0)

Open Ended

How can you describe the graph of f(x) compared to the graph of f(x), if a is a negative number?

If a is negative then the graph f(x)...........

If a is positive then the graph f(x)..........