The function $f$ is given in three equivalent forms.
Which form most quickly reveals the vertex?
Choose 1 answer:
(A) $f(x)=\frac{1}{2}(x-5)^{2}-2$
(B) $f(x)=\frac{1}{2} x^{2}-5 x+\frac{21}{2}$
(C) $f(x)=\frac{1}{2}(x-3)(x-7)$

What is the vertex?
Vertex $=(\square, \square)$

Question

The function $f$ is given in three equivalent forms.
Which form most quickly reveals the vertex?
Choose 1 answer:
(A) $f(x)=\frac{1}{2}(x-5)^{2}-2$
(B) $f(x)=\frac{1}{2} x^{2}-5 x+\frac{21}{2}$
(C) $f(x)=\frac{1}{2}(x-3)(x-7)$

What is the vertex?
Vertex $=(\square, \square)$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the form that most quickly reveals the vertex of the parabola. ‖ ‖ step 2 ⋮ Form A, $f(x) = \frac{1}{2}(x - 5)^2 - 2$, is already in vertex form. ‖ ‖ step 3 ⋮ The vertex form of a parabola is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. ‖ ‖ step 4 ⋮ For Form A, $h = 5$ and $k = -2$, so the vertex is $(5, -2)$. ‖ ∻1 Answer∻ ⚹ The form that most quickly reveals the vertex is Form A, and the vertex is $(5, -2)$. ⚹ ∻Key Concept∻ ⚹Vertex Form of a Parabola⚹ ∻Explanation∻ ⚹The vertex form of a parabola, $f(x) = a(x - h)^2 + k$, directly gives the vertex as the point $(h, k)$. Form A is already in this format, making it the quickest way to identify the vertex.⚹◊What is the formula to find the vertex of a quadratic function?⍭ Generate me a similar question◊

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