Question

the function d(x) is shown in the graph.
write the equation of d(x) in vertex form.

• d(x) = (x + 3)^2 - 1
• d(x) = (x + 3)^2 + 1
• d(x) = (x - 3)^2 - 1
• d(x) = (x - 3)^2 + 1

Explanation:

Identify the vertex from the graph

$$ (h, k) = (3, -1) $$

Write the vertex form equation

$$ d(x) = a(x - h)^2 + k $$

$$ d(x) = a(x - 3)^2 - 1 $$

Determine the leading coefficient using a point on the graph

Using the point \((1, 3)\):

$$ 3 = a(1 - 3)^2 - 1 $$

$$ 3 = 4a - 1 $$

$$ 4 = 4a \implies a = 1 $$

$$ d(x) = (x - 3)^2 - 1 $$

Answer:

• (A) \(d(x) = (x + 3)^2 - 1\)
• (B) \(d(x) = (x + 3)^2 + 1\)
• (C) \(d(x) = (x - 3)^2 - 1\) (Correct answer)
• (D) \(d(x) = (x - 3)^2 + 1\)