The a-value of the quadratic equation is found by using the x-intercepts and a given point on the graph. After forming the equation and substituting the given point into it, we solve for a to get -1/2.
The student is asked to find the a-value of a quadratic equation with specific x-intercepts and a point through which it passes. A standard form of a quadratic equation is ax^2 + bx + c = 0. The x-intercepts (-3,0) and (5,0) indicate that the factors of the quadratic equation are (x + 3) and (x - 5). Therefore, the quadratic equation can be written as a(x + 3)(x - 5). To find the a-value, we need to use the point (3,6). Substituting this point into the equation gives us a(3 + 3)(3 - 5) = 6. Simplifying, we get 6a(-2) = 6, which further simplifies to -12a = 6. Solving for a, we get a = -1/2.