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Math 1 Summer Bridge

Day 8: Quadratic Relationships

Recognize quadratic patterns and connect them to parabolas and squared terms.

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Student Goal

I can identify quadratic relationships from equations, tables, and graphs.

Why It Matters

Quadratic relationships are central in Math 1. They model curved patterns such as area, projectiles, and maximum or minimum values.

Warm-Up

Warm-Up 1

Which equation is quadratic?

Warm-Up 2

Find 3^2.

Short Lesson

Standard Focus

NC.M1.F-IF.7 and NC.M1.F-BF.1: Quadratic functions

Student-Friendly Standard Goal

I can recognize and interpret key features of simple quadratic relationships.

  • A quadratic equation includes a squared variable, such as x^2.
  • The graph of a quadratic function is a parabola.
  • In tables, quadratic relationships often have constant second differences.
  • The vertex is the turning point of the parabola.

Guided Examples

Guided Example 1

Evaluate a Quadratic

Evaluate f(x) = x^2 - 4 when x = -3.

Step 1

f(-3) = (-3)^2 - 4

What is (-3)^2?

Guided Example 2

Identify the Vertex

Use the table for y = (x - 1)^2 + 2 to identify the vertex.

Step 1

6, 3, 2, 3, 6

Which y-value is the minimum?

Practice

Problem 1

The graph of a quadratic function is usually called a...

Problem 2

Evaluate x^2 + 1 when x = 4.

Problem 3

Which table may be quadratic?

Problem 4

Error analysis: A student says (-5)^2 = -25. What is wrong?

Problem 5

True or false: y = 6x - 1 is quadratic.

Reflection

How are you feeling about today's skill?

Optional reflection: What is one step, word, or representation from today that you want to remember when Math 1 starts?