Question

The function ggg is given in three equivalent forms. Which form most quickly reveals the vertex? Choose 1 answer: Choose 1 answer: (Choice A) A g(x)=\dfrac{1}{2}(x-8)^2-8g(x)= 2 1 ​ (x−8) 2 −8g, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction, left parenthesis, x, minus, 8, right parenthesis, squared, minus, 8 (Choice B) B g(x)=\dfrac{1}{2}(x-12)(x-4)g(x)= 2 1 ​ (x−12)(x−4)g, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction, left parenthesis, x, minus, 12, right parenthesis, left parenthesis, x, minus, 4, right parenthesis (Choice C) C g(x)=\dfrac{1}{2}x^2-8x+24g(x)= 2 1 ​ x 2 −8x+24g, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction, x, squared, minus, 8, x, plus, 24 What is the vertex? Vertex = ((left parenthesis ,,comma ))right parenthesis

Answer 1

Answer:

$(A)g(x)=\dfrac{1}{2}(x-8)^2-8$

(h,k)=(8,-8)

Step-by-step explanation:

$(A)g(x)=\dfrac{1}{2}(x-8)^2-8\\(B)g(x)=\dfrac{1}{2}(x-12)(x-4)\\(C)g(x)=\dfrac{1}{2}x^2-8x+24$

From the given equivalent forms of the function g(x), we are to pick which form quickly reveals the vertex.

The vertex form of a parabola is given: $f (x) = a(x - h)^2 + k$, where (h, k) is the vertex of the parabola.

Therefore, Option A, $(A)g(x)=\dfrac{1}{2}(x-8)^2-8$ quickly reveals the vertex.

From the above, h=8, k=-8. Therefore the vertex (h,k)=(8,-8)