1 Find a quadratic function in standard form fx ax h2 k th

1. Find a quadratic function in standard form f(x) = a(x h)² + k that satisfies the given conditions. the vertex of the graph of f is (2, 5), graph passes through (3, 2)

f(x) =

1a. Find a quadratic function f(x) = ax² + bx + c that satisfies the given conditions. graph passes through (3, 1), zeros of f are 2 and 4

f(x)=

Solution

1) f(x) = a(x- h)^2 +k where (h, k) is vertex

Vertex : ( 2, 5)

So, equation becomes : f(x) = a(x-2)^2 + 5

Calculate a: 2 = a(3-2)^2 +5

2 = a+5 ---> a = -3

f(x) = -3(x-2)^2 +5

1a) f(x) = ax2 + bx + c that satisfies the given conditions. graph passes through (3, 1), zeros of f are 2 and 4

we can write f(x) also as : f(x) = k(x-a)(x-b)

So, f(x) = k(x-2)(x-4)

Now use (3, -1) to find k:

-1 = k(3-2)(3-4)

-1 = -1*k----> k =1

f(x) = (x-2)(x-4) = x^2 -6x +8