I am stumped could someone please explain this problem?

Give the solutions to the following quadratic equation by examining the graph of the related quadratic function:
Graph: y=x^2+2x-15
Equation: x^2+2x-15=0
Thanks so much.

algebraic solution:

(x+5)(x-3) = 0
so x = -5 or x = 3

When you graphed it, did you not get a parabola that opened upwards and crossed the x-axis at -5 and 3 ?

We can't draw graphs for you; you can and should do that yourself.

Since the equation can be factored to (x+5)(x-3) = 0,
the solutions are x=-5 and +3.

To find the solutions to the quadratic equation x^2 + 2x - 15 = 0 by examining the graph of the related quadratic function y = x^2 + 2x - 15, you can follow these steps:

1. Plot the graph of the quadratic function y = x^2 + 2x - 15 on a coordinate plane. To do this, you can start by finding the vertex, which is the point where the parabola reaches its minimum or maximum value. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function in the form ax^2 + bx + c. In this case, a = 1, b = 2, and c = -15.

x = -2 / (2 * 1) = -1

Substitute the x-coordinate of the vertex back into the equation to find the y-coordinate:

y = (-1)^2 + 2(-1) - 15
= 1 - 2 - 15
= -16

So, the vertex is (-1, -16).

2. Next, plot a few more points on the graph to get a better idea of the shape of the parabola. You can choose values for x, substitute them into the equation y = x^2 + 2x - 15, and calculate the y-values. For example, you can choose x = -3, -2, -1, 0, 1, 2, and 3. Calculate the corresponding y-values for each x-value and plot those points on the graph.

3. Now, examine the graph and look for the x-intercepts, which are the points where the parabola intersects the x-axis. These points represent the solutions to the quadratic equation. By observing the graph, you can see that the parabola crosses the x-axis at x = -5 and x = 3.

Therefore, the solutions to the quadratic equation x^2 + 2x - 15 = 0 are x = -5 and x = 3, as indicated by the x-intercepts on the graph of the quadratic function y = x^2 + 2x - 15.