Multiple Representations Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard

A graph passes through

(-2,0)

(0,-4)

, and

(1,0)

and appears to be a parabola. Find the quadratic equation and verify using all three points.

Solution

1
The $x$ -intercepts $-2$ and $1$ give factors $(x+2)(x-1)$ , so $f(x) = a(x+2)(x-1)$ .
2
Use $y$ -intercept $(0,-4)$ : $f(0)=a(2)(-1)=-2a=-4 \Rightarrow a=2$ . So $f(x)=2(x+2)(x-1)=2x^2+2x-4$ .
3
Verify: $f(-2)=2(0)(-3)=0$ ✓; $f(0)=2(2)(-1)=-4$ ✓; $f(1)=2(3)(0)=0$ ✓.

Answer

f(x) = 2x^2 + 2x - 4

Graph information (intercepts) provides constraints to determine the algebraic formula. Using the factored form from

x

-intercepts and the

y

-intercept to find the leading coefficient is an efficient strategy.

About Multiple Representations

Every function can be expressed in four equivalent ways: as an algebraic formula, a table of input-output pairs, a graph on the coordinate plane, or a verbal description. Each representation highlights different properties and is useful in different contexts.

Learn more about Multiple Representations →

More Multiple Representations Examples

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Represent the function [formula] in four ways: equation, table of values, graph description, and ver

Example 2 medium

A table gives values: [formula] and [formula]. Identify the function type, write its equation, and d

Example 3 easy

Convert the verbal description to an equation: 'The output is three less than twice the square of th

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Related Concepts

Function Coordinate Plane