Negative Inputs

Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 2 of 55.

$The curve y = x squared plus 3x, with the point (-2, -2) marked below the x-axis$

Every point on a graph is (x, f(x)). So an output is a height. On $y = {x}^{2}+3x$ , the point at x = -2 has height -2. It is below the x-axis.

To get this from the rule, put -2 in brackets, with its minus sign: $\left(-2\right)^2 + 3 \cdot \left(-2\right) = 4 - 6 = -2$ .

Without brackets, $-{2}^{2}$ means the minus of 2 squared. That is -4, not 4. This mistake gives -10, and the graph shows that -10 is wrong.

Challenge

How high is the curve $h\left(x\right) = {x}^{2}-4x+1$ at $x = -5$ ? Use the rule. Then work out $h\left(-5\right)$ one line at a time.

Try it yourself

h\left(-5\right)

Simplify

Given $h\left(x\right) = x^{2}-4x+1$

All lessons in Functions & Transformations

1Rules That Draw

4Combining Functions

7Shifting Graphs

10Functions in Stories

2Expressions as Inputs

5Composition

8Stretching and Flipping

11Final Challenges

3Domain and Range

6Inverse Functions

9Rate of Change