Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.
Identify quadratic x-intercepts and zeros
Problem
From this quadratic graph or rule, identify the \(x\text{-}\text{intercepts}\) and interpret them as zeros: \(y=(x-2)(x+4)\).
Big Picture
What this problem is really about
Zeros are input values, while x-intercepts are the corresponding points on the axis. We’ll set the factored output equal to zero, solve each factor with careful attention to its sign, and verify that each value makes the product vanish. Then we’ll translate those inputs into ordered pairs by attaching the required zero output.
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