y = x^2 + 2x - 8: which form shows where it crosses the y axis Step by Step

Step by step

The question

Question: which form of y = x² + 2x − 8 shows where it crosses the y axis?

y = x² + 2x − 8

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)

It is already in standard form.

2 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: −8.

on the y axis, x = 0: y = 0² + 2 × 0 − 8 = −8

Careful!

Not (−8, 0).

A point is written x first, then y.

Here x is 0 and y is −8.

Careful: not (−8, 0) ✗

So it crosses the y axis at (0, −8).

point = (0, −8)

3 Show it on the graph

Here is the graph of y = x² + 2x − 8.

It crosses the y axis at (0, −8).

4 Check

Let's check in the question's own form, y = x² + 2x − 8.

x = 0 gives y = −8: the point on the y axis.

So it is right!

x = 0: y = 0² + 2 × 0 − 8 = 0 + 0 − 8 = −8

Let's look back.

First: pick the form.

Then: read the y axis crossing.

Then: show it on the graph.

Last: check.

Answer