Find the vertex of the graph of the following quadratic function.

The vertex is
(Type an ordered pair.)

Question

Find the vertex of the graph of the following quadratic function. $$ f(x)=3 x^{2}+6 x-8 $$ The vertex is (Type an ordered pair.)

UpStudy AI · Accepted Answer

1. The quadratic function is given by $$ f(x) = 3x^2 + 6x - 8 $$.

2. For a quadratic function in the form $$ ax^2 + bx + c $$, the $$ x $$-coordinate of the vertex is given by:
   $$
   x = -\frac{b}{2a}
   $$
   Here, $$ a = 3 $$ and $$ b = 6 $$, so:
   $$
   x = -\frac{6}{2 \times 3} = -\frac{6}{6} = -1
   $$

3. Substitute $$ x = -1 $$ into $$ f(x) $$ to find the $$ y $$-coordinate:
   $$
   f(-1) = 3(-1)^2 + 6(-1) - 8 = 3(1) - 6 - 8 = 3 - 6 - 8 = -11
   $$

4. Therefore, the vertex of the graph is:
   $$
   (-1, -11)
   $$
The vertex of the graph is $$(-1, -11)$$.

Find the vertex of the graph of the following quadratic function.

The vertex is
(Type an ordered pair.)

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Answer

Solution

Beyond the Answer

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Find the vertex of the graph of the following quadratic function. The vertex is (Type an ordered pair.)

Upstudy AI Solution

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Solution

Beyond the Answer

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Find the vertex of the graph of the following quadratic function.

The vertex is
(Type an ordered pair.)