1Cademy - Finding Points on the Graph of $$ f(x) = x^2 + 2x

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Solving a Quadratic Equation by Factoring

Example

Finding Points on the Graph of $f(x) = x^2 + 2x - 2$ when $f(x) = 6$

To find $x$ when $f(x) = 6$ for the polynomial function $f(x) = x^2 + 2x - 2$ , substitute $6$ for $f(x)$ to create the equation $6 = x^2 + 2x - 2$ . Put the quadratic equation in standard form by subtracting $6$ from both sides, yielding $x^2 + 2x - 8 = 0$ . Factor the trinomial to obtain $(x + 4)(x - 2) = 0$ . Apply the Zero Product Property to solve for $x$ , which gives $x + 4 = 0$ or $x - 2 = 0$ , resulting in $x = -4$ and $x = 2$ . Because $f(-4) = 6$ and $f(2) = 6$ , the two points that lie on the graph of the function are $(-4, 6)$ and (2, 6).