Answer: y = 8x^2
Explanation:
The equation we need to model is for a parabola that opens upward, meaning the a-value must be positive. Additionally, the vertex of the parabola is located at the origin, meaning the vertex is (0,0). This tells us that the equation of the parabola takes the form y = ax^2.
To find the value of a, we need to use the information given, which is that the focus (where the bulb is located) is 8 in from the vertex. We know that the focus of a parabola is (a,0), and the vertex is (0,0). Using the distance formula, we can find the value of a.
Distance Formula: d = √((x_1-x_2)^2 + (y_1-y_2)^2)
d = √((a - 0)^2 + (0 - 0)^2)
d = √(a^2)
d = a
So, we can set a = 8. This gives us the following equation: y = 8x^2
Therefore, the equation of the parabola that models the cross section of the light reflector is:
y = 8x^2