Question

The $x$-intercepts of the parabola $y = x^2 + bx + c$ are $(-3,0)$ and $(5,0).$ Find the equation of the parabola, and submit your answer in $y = ax^2 + bx + c$ form.

Answer 1

Answer:

y = x^2 - 2x - 15

Step-by-step explanation:

Since the x-intercepts are (-3,0) and (5,0), the roots of the quadratic are -3 and 5. This means that the equation of the parabola is

y = (x + 3)(x - 5), which expands to  y = x^2 - 2x - 15

Answer 2

The $x$-intercepts of the parabola $\rm \ y = x^2 + bx + c$ are $(-3,0)$ and $(5,0)$.

The equation of the parabola, and submit your answer in $y = ax^2 + bx + c$ form will be $\rm y = x^2 - 2x - 15$

Given :

            $\rm \ y = x^2 + bx + c \ (\ \times \ \;intercepts ) \\\\\ (-3,0)\ \;\;\; \& \;\;\; \ (5,0)$

We knows that the x-intercepts are (-3,0) and (5,0), then the roots of the quadratic are -3 & 5  i.e. The equation of the parabola will be

To find the focus of any parabola we know that the equation of any parabola in a vertex form will be y=a(x−h)2+k where,  a is the slope of the equation.

According to the question,

y = (x + 3)(x - 5) i.e.

Therefore, The equation of the parabola $\rm y = x^2 - 2x - 15$ .

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