Section 5-1: Graphing Quadratic Functions in Standard Form

Goal: Graph quadratic functions in the form y = ax2+ bx + c

Warm-UpsFind the x – intercept and the y – intercept:

1. 3x – 5y = 15 x – intercept: 5 y – intercept: -3

2. y = 2x + 7x – intercept: -7/2 y – intercept: 7

Quadratic FunctionA function that can be written in the standard

form y = ax2+ bx + c where a ≠ oThe graph of a quadratic function is a

parabolaThe graph of y = x2:

Steps to Solving a Quadratic Function Using a Table

Step 1: Make a table of values.

Step 2: Plot the points from the table.

Step 3: Draw a smooth curve through the points.

Example 1: Graph a Quadratic Function Using a TableGraph: y = ½x2 – 1

X -4 -2 0 2 4

Y

Checkpoint: Graph a Quadratic Function Using a TableGraph: y = -3x2

X -2 -1 0 1 2

Y

Checkpoint: Graph a Quadratic Function Using a TableGraph: y = -x2 – 2

X -2 -1 0 1 2

Y

Checkpoint: Graph a Quadratic Function Using a TableGraph: y = ¼ x2 + 3

X -4 -2 0 2 4

Y

Example 2: Graph a Quadratic Function in Standard Formy = x2 – 6x + 5

Example 2: Graph a Quadratic Function in Standard Formy = -x2 – 2x + 1

Example 2: Graph a Quadratic Function in Standard Formy = 2x2 + x - 1

Multiplying BinomialsMonomial – a number, a variable or the

product of a number and one or more variables with whole number exponents.

Binomial – the sum of two monomialsThe FOIL is used to multiply binomials:

First termsOuter termsInner termsLast terms

Example 3: Multiply BinomialsFind the product (2x + 3)(x – 7).

Checkpoint: Find the product.a. (x – 4)(x + 6) b. (3x + 1) (x – 1)

Example 4: Write a Quadratic Function in Standard FormWrite the function y = 2(x – 2)2 + 5

Checkpoint: Write the function in standard form.a. y = 2(x + 1)(x – 3) b. Y = 3(x – 4) (x – 6)

Homework:p. 225 – 227

16 – 64 even, 71 – 74 all