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dmitriy555 [2]
3 years ago
12

Write an equation for a quadratic function in vertex form with

Mathematics
1 answer:
il63 [147K]3 years ago
5 0

Answer:

\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6

Step-by-step explanation:

We want to write the equation for a quadratic function in vertex form with vertex at (-1, 6) that passes through the point (-3, 4).

Vertex form is given by:

\displaystyle f(x)=a(x-h)^2+k

Where (<em>h, k</em>) is the vertex and <em>a</em> is the leading coefficient.

Since our vertex is at (-1, 6), <em>h</em> = -1 and <em>k</em> = 6. Substitute:

f(x)=a(x-(-1))^2+(6)

Simplify:

f(x)=a(x+1)^2+6

Next, since the quadratic passes through the point (-3, 4), f(x) = 4 when <em>x</em> = -3. Substitute:

(4)=a(-3+1)^2+6

Solve for <em>a</em>. Simplify:

-2=a(-2)^2

Hence:

\displaystyle -2=4a\Rightarrow a=-\frac{1}{2}

Therefore, our function in vertex form is:

\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6

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