y = (x - 1)(x - 5): which form shows where it crosses the y axis Step by Step

Step by step

The question

Question: which form of y = (x − 1)(x − 5) shows where it crosses the y axis?

y = (x − 1)(x − 5)

1 Pick the form

A parabola can be written in three forms.

Each one shows one thing at a glance.

On the y axis, x is 0.

In the standard form, x = 0 makes every x part 0, so c is left.

So the standard form shows where it crosses the y 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)

2 Open the brackets

Open the brackets: each part of the first times each part of the second.

x times x is x squared.

x times −5 is −5x.

−1 times x is −x.

−1 times −5 is 5.

(x − 1)(x − 5) = x² − 5x − x + 5

The two x parts are like terms.

Together they make −6x.

−5x − x = −6x

So y = x² − 6x + 5.

That is the standard form.

y = x² − 6x + 5

3 Read the y axis crossing

On the y axis, x is 0.

With x = 0, every x part is 0.

Only the plain number is left: 5.

on the y axis, x = 0: y = 0² − 6 × 0 + 5 = 5

Careful!

Not (5, 0).

A point is written x first, then y.

Here x is 0 and y is 5.

Careful: not (5, 0) ✗

So it crosses the y axis at (0, 5).

point = (0, 5)

4 Show it on the graph

Here is the graph of y = x² − 6x + 5.

It crosses the y axis at (0, 5).

5 Check

Let's check in the question's own form, y = (x − 1)(x − 5).

x = 0 gives y = 5: the point on the y axis.

So it is right!

x = 0: y = (0 − 1)(0 − 5) = (−1) × (−5) = 5

Let's look back.

First: pick the form.

Then: open the brackets.

Then: read the y axis crossing.

Then: show it on the graph.

Last: check.

Answer