Final answer:
To find the quadratic equation for a function with a vertex of (3,4) and a point at (5,8) in standard form, we can use the vertex form of a quadratic equation and substitute the given values. The resulting equation is y = 2x^2 - 12x + 18.
Step-by-step explanation:
To find the quadratic equation for a function with a vertex of (3,4) and a point at (5,8) in standard form, we can use the vertex form of a quadratic equation, which is y = a(x-h)^2 + k. The vertex form gives us the vertex coordinates as (h, k).
Substituting the given vertex values, we have y = a(x-3)^2 + 4. Now we can use the point (5,8) to find the value of 'a'. Substituting the point values, we get 8 = a(5-3)^2 + 4. Simplifying this equation, we find a = 2.
Substituting the value of 'a' back into the vertex form, we get the quadratic equation:
y = 2(x-3)^2 + 4.
Expanding and rearranging the terms, we get the equation:
y = 2x^2 - 12x + 18.