Find the quadratic function that has the vertex (4,5) and passes through the point (8,21) If possible, can you explain the work?

Question

snow_lady [41]

4 years ago

14

Find the quadratic function that has the vertex (4,5) and passes through the point (8,21) If possible, can you explain the work?

Thanks! *71 POINTS!*

Mathematics

1 answer:

Ganezh [65] · Answer 1 · 2022-01-14T03:03:30+03:00

Start by looking at the vertex form of a quadratic function, f(x) = a(x - h)^2 + k. The variables h and k are the values of the vertex. Plug those in to get f(x) = a(x - 4)^2 + 5. To find the variable a, plug in the point given for the x and y values. So, you get (21) = a((8) - 4)^2 + 5. Solve for a algebraically, and you get a = 1. Finally, plug everything in and simplify the equation. You should get that the quadratic function is f(x) = x^2 - 8x + 21. Hope this helps!