Parabola Basics

Parabola Basics

J Dunn 2021

Multiple Choice

Quick review question: What is (x + 3)(x + 5)?

• 3x² + 2x + 15

• x² + 15

• x² + 8

• x² + 8x + 15

Today you will learn about parabolas

A parabola is a U-Shaped graph. The real world is full of these shapes, such as kicking a football, the terrain in a valley, and the orbit of planets.

The goal is to model these things using equations so that we can make predictions

The vertex is the turning point of a parabola. Here, it is called a maximum point because it's the highest the ball goes

Multiple Choice

What is the maximum point of this parabola?

• (3, 5)

• (5, 3)

• (5, 0)

• (1, 0)

The vertex can also be a minimum point.

Multiple Choice

What is the minimum point of this parabola?

• (0, 7)

• (2, 3)

• (-2, 3)

• (3, 5)

The vertex is the turning point

Minimum and Maximum points are different styles of vertex

Some parabolas

Open Upward

Some parabolas

Open Down

Multiple Choice

When you throw a basketball through the air, the path it follows is a parabola. The parabola opens...

• UP

• DOWN

X-intercepts AKA Zeros

• Zeros is another name for x-intercepts because the y-coordinate there is 0

• Parabolas can have 0, 1, or 2 zeros

• Most real world stuff has two

Open Ended

This pictures shows a decorative water fountain. Describe the x-intercepts. What happens at the x-intercepts?

Multiple Select

Select the x-intercepts of this graph.

• (0, 6)

• (-2, 0)

• (-5, 0)

• (-4, -2)

All parabolas have symmetry

• The "axis of symmetry" cuts right down the middle and intersects the vertex

• It has an equation like any other vertical line

• x = 6

Multiple Choice

What is the equation for the axis of symmetry?

• x = 3

• y = 3

• y = 5

• x = 5

Multiple Choice

What is the equation for the axis of symmetry?

• x = 2

• x = -2

• x = 3

• y = 7

The St. Louis Arch is a parabola