Determine which coordinate is the vertex of without graphing the
parabola.

Ask by Gross Cole. in Canada

Dec 10,2024

Question

Determine which coordinate is the vertex of $$ f(x)=4 x^{2}-8 x+11 $$ without graphing the parabola.

UpStudy AI · Accepted Answer

To find the vertex of the quadratic function $$ f(x) = 4x^2 - 8x + 11 $$, we can use the vertex formula. The x-coordinate of the vertex for a quadratic function in the form $$ ax^2 + bx + c $$ is given by:

$$
x = -\frac{b}{2a}
$$

In this case, we have:

- $$ a = 4 $$
- $$ b = -8 $$

Now, we can substitute these values into the formula:

$$
x = -\frac{-8}{2 \cdot 4} = \frac{8}{8} = 1
$$

Next, we need to find the y-coordinate of the vertex by substituting $$ x = 1 $$ back into the function $$ f(x) $$:

$$
f(1) = 4(1)^2 - 8(1) + 11
$$
$$
= 4(1) - 8 + 11
$$
$$
= 4 - 8 + 11
$$
$$
= 7
$$

Thus, the vertex of the function $$ f(x) = 4x^2 - 8x + 11 $$ is at the coordinate:

$$
\boxed{(1, 7)}
$$
The vertex of $$ f(x)=4 x^{2}-8 x+11 $$ is at the coordinate (1, 7).

Determine which coordinate is the vertex of without graphing the
parabola.

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Determine which coordinate is the vertex of without graphing the parabola.