Test 10 section 4 number 28

In this question, you’re given the equation of a parabola in factored form: f(x)=(x+3)(x-k). Setting aside the unknown constant k, there’s a lot we know from looking at the equation.

First, we know the parabola opens upwards, because when that binomial is FOILed out, the x^2 term will be positive.

Second, we know that the function has a zero (which means the parabola has an x-intercept at x=-3.

The question asks us to pick a graph that could could represent the parabola, so let’s look at our choices.

  • Choices A and B open downwards, so they’re out.
  • Choice C opens upwards, but it doesn’t have an x-intercept at x=-3, so it’s out, too.
  • Choice D is correct. It opens upwards and it has an x-intercept at x=-3.

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