A quadratic curve y=x^2+bx+c has roots x= -2 and x=7.5. Determine the value of c.

To determine the value of $c$ for the quadratic curve $y = x^2 + bx + c$ with roots $x = -2$ and $x = 7.5$, follow these steps:

1. Use the fact that the roots of the quadratic equation are given: The roots of the quadratic equation $ax^2 + bx + c = 0$ can be written in factored form as: $(x - \alpha)(x - \beta) = 0$ where $\alpha$ and $\beta$ are the roots. For this problem, $\alpha = -2$ and $\beta = 7.5$.

2. Write the quadratic equation in its factored form: $(x + 2)(x - 7.5) = 0$

3. Expand the factored form to get the standard form: $(x + 2)(x - 7.5) = x^2 - 7.5x + 2x - 15 = x^2 - 5.5x - 15$

4. Compare the expanded form with the given quadratic equation: The given quadratic equation is $y = x^2 + bx + c$. From the expanded form, we have: $x^2 - 5.5x - 15$ By comparing coefficients, we see that $b = -5.5$ and $c = -15$.

Therefore, the value of $c$ is $-15$.