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Sketch the graph of y = x squared + 2 x minus 15 using your graphing calculator. What are the x-intercepts of this graph?
a.
(-5, 0) and (3, 0)
c.
There are no x-intercepts
b.
(2, 0) and (-2, 0)
d.
(9, 0) and (-2, 0)

Respuesta :

The x-intercepts of the quadratic function y = x² + 2x - 15 are:

a. (-5, 0) and (3, 0).

The graph is sketched at the end of the answer;

What is a quadratic function?

A quadratic function is given according to the following rule:

y = ax² + bx + c

The solutions are:

  • [tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
  • [tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

In this problem, the function is:

y = x² + 2x - 15.

The coefficients are:

a = 1, b = 2, c = -15.

Hence:

  • [tex]\Delta = 2^2 - 4(1)(-15) = 64[/tex]
  • x1 = (-2 + 8)/2 = 3.
  • x2 = (-2 - 8)/2 = -5.

Hence the x-intercepts are:

a. (-5, 0) and (3, 0).

More can be learned about quadratic functions at https://brainly.com/question/24737967

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