Final answer:
To write the equation for the quadratic function, we use the given points and the y-intercept. Three equations can be formed using these points, and the values of a, b, and c can be solved from the equations, resulting in the quadratic equation y = 0.04x^2 - 0.7x + 10.
Step-by-step explanation:
To write an equation for the quadratic function that goes through the points (-16,2) and (4,2), and has a y-intercept of (0,10), we can use the general form of a quadratic function, which is given by y = ax^2 + bx + c. Since the y-intercept is (0,10), we know that when x = 0, y = 10. Plugging these values into the equation, we get 10 = a(0)^2 + b(0) + c, which simplifies to c = 10. Now, let's use the other two given points to form two equations that we can solve simultaneously for the values of a and b.
Using the point (-16,2), we have 2 = a(-16)^2 + b(-16) + 10, which simplifies to 256a - 16b + 10 = 2.
Using the point (4,2), we have 2 = a(4)^2 + b(4) + 10, which simplifies to 16a + 4b + 10 = 2.
Solving these two equations, we get a = 0.04 and b = -0.7. So, the equation for the quadratic function is y = 0.04x^2 - 0.7x + 10.