Introduction to Quadratics

Quadratic Functions!

Instructions:

You can use your notes or your textbook (Ch 8 and 9) or the internet to help you answer the following questions.

Multiple Choice

Which of the equations is a "Quadratic Equation?"

• y=2x+3

• y = x² + 3x - 4

• y = x³

• y = 1/2x

Quadratic Equations have a "degree" of 2.

A degree is the biggest exponent in an equation. When a number is written in small print above and to the right of another number, it is an exponent. You can see in the illustration that the degree is 2.

All quadratics have a parabola shape and can be written as an equation with a degree of 2.

Not all curves are parabolas. For example, the St. Louis arch is a "catenary curve" which looks like a parabola, but it is not! Oh well, nothing's perfect.

Multiple Choice

What is general standard form of a quadratic?

• y=ax²+bx+c

• y=mx+b

• y=(x+h)(x+k)

• y=a(x+h)²+k

Multiple Choice

What is the factored form of a quadratic?

• y=ax²+bx+c

• y=mx+b

• y=(x+h)(x+k)

• y=a(x+h)²+k

Multiple Choice

What is the vertex form of a quadratic?

• y=ax²+bx+c

• y=mx+b

• y=(x+h)(x+k)

• y=a(x+h)²+k

Multiple Choice

Which of the equations is NOT a quadratic equation at all?

• y=ax²+bx+c

• y=mx+b

• y=(x+h)(x+k)

• y=a(x+h)²+k

The quadratic formula can solve any quadratic equation for x.

Quadratic Formula

Multiple Choice

What are the solutions for the quadratic equation?

• Where the top of the graph is.

• Where it crosses the y-axis

• y=x²

• -4 and 0

Multiple Choice

What is the vertex of the quadratic?

• Where the top of the graph is.

• Where it crosses the y-axis

• y=x²

• -4 and 0

Multiple Choice

What is the parent function for all quadratics?

• Where the top of the graph is.

• Where it crosses the y-axis

• y=x²

• -4 and 0

Overview: Read Carefully

We are going to learn to graph quadradic functions and to solve quadratic equatiaons.

In order to graph quadratics, we need to write the factored form of a quadratic. If the quadratic doesn't factor nicely, then the solutions (where it crosses x) are decimals and we need the quadratic formula or completing the square to solve for x.