y = (x + 3)(x - 1): which form shows where it crosses the x axis Step by Step

Step by step

The question

Question: which form of y = (x + 3)(x − 1) shows where it crosses the x axis?

y = (x + 3)(x − 1)

1 Pick the form

A parabola can be written in three forms.

Each one shows one thing at a glance.

On the x axis, y is 0.

The factored form is a product, and a product is 0 when one bracket is 0.

So the factored form shows where it crosses the x axis.

standard: ax² + bx + c → y axis at c

factored: a(x − r)(x − s) → x axis at r and s ✓

vertex: a(x − h)² + k → turning point (h, k)

It is already in factored form.

2 Read the x axis crossings

On the x axis, y is 0.

So the product must be 0.

on the x axis, y = 0: (x + 3)(x − 1) = 0

A product is 0 only when one of its parts is 0.

x + 3 is 0 when x = −3.

x − 1 is 0 when x = 1.

A × B = 0 → A = 0 or B = 0

x + 3 = 0 → x = −3

x − 1 = 0 → x = 1

Careful!

Not 3.

x + 3 is 0 when x is −3: the sign in the bracket is the opposite.

Careful: not (x + 3): x = 3 ✗

So it crosses the x axis at x = −3 and x = 1: the points (−3, 0) and (1, 0).

points = (−3, 0) and (1, 0)

3 Show it on the graph

Here is the graph of y = x² + 2x − 3.

It crosses the x axis at −3 and 1.

4 Check

Let's check in the question's own form, y = (x + 3)(x − 1).

x = −3 gives y = 0: on the x axis.

x = −3: y = ((−3) + 3)((−3) − 1) = 0 × (−4) = 0

And x = 1 gives y = 0: on the x axis.

So it is right!

x = 1: y = (1 + 3)(1 − 1) = 4 × 0 = 0

Let's look back.

First: pick the form.

Then: read the x axis crossings.

Then: show it on the graph.

Last: check.

Answer