Question

Vihaan finds that the roots of a quadratic equation that contains a difference of squares pattern is x = +-16. What is true about the graph of the parabola described by the quadratic equation?
The graph contains two parabolas: one that touches the x-axis at x = 16 and one that touches the x-axis at x = -16.
The parabola crosses the x-axis at x = +-16.
The graph contains a parabola that does not have a vertex.
The parabola does not touch or cross the axis.

Answer 1

The answer to the question, What is true about the graph of the parabola described by the quadratic equation is that the parabola crosses the x-axis at x = ±16.

Since the quadratic equation has roots x = ±16, it implies that its factors are x - 16 and x + 16.

So, the quadratic equation is y = (x - 16)(x + 16) = x² - 16²

Also, we know that the roots of a quadratic equation are the points where the value of the quadratic equation equals zero. At this value, the quadratic equations crosses the x-axis at the roots of the quadratic equation.

Since the roots of our quadratic equation are x = ±16, it implies that the parabola crosses the x-axis at x = ±16.

So, the answer to the question, What is true about the graph of the parabola described by the quadratic equation is that the parabola crosses the x-axis at x = ±16.

Learn more about quadratic equations here:

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