7.10.4 Using the Standard Form of an Equation to Find the x- and y-intercepts

Algebra 17.10.4 Using the Standard Form of an Equation to Find the x- and y-intercepts

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The equations $y = x^{2} + 6 x + 8$ and $y = (x + 2) (x + 4)$ both define the same quadratic function.

Without graphing, identify the $x$ -intercepts of the graph. Explain how you know.

Compare your answer:

$(- 2, 0)$ , $(- 4, 0)$ ; The constants in the factors of an equation in factored form give a clue about where the $x$ -intercepts are when the equation is graphed. In the equation $y = (x + 2) (x + 4)$ , the $x$ -intercepts are $(- 2, 0)$ and $(- 4, 0)$ .

Without graphing, identify the $y$ -value of the $y$ -intercept of the graph. Be prepared to show your reasoning.

Compare your answer:

8; The $y$ -intercepts of the graph can be seen when the equation is in standard form. The $y$ -coordinate is the number without the variable. In the equation $y = x^{2} + 6 x + 8$ , it is the 8 so the $y$ -intercept is $(0, 8)$ .

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