Determine the vertex of the graph of the quadratic function .

Question

Determine the vertex of the graph of the quadratic function  .

Quizplus · Accepted Answer

To find the vertex of a quadratic function in the form of $f(x) = ax^2 + bx + c$, we use the formula $x=-\frac{b}{2a}$ to find the $x$-coordinate of the vertex, and then substitute it into the equation to find the $y$-coordinate.

In this case, the quadratic function is $f(x) = 4x^2 - 16x + 17$. We can see that $a = 4$ and $b = -16$. Substituting these values into the formula, we get:

$x = -\frac{-16}{2\cdot4} = 2$

Now we substitute $x=2$ into the equation to find the $y$-coordinate:

$f(2) = 4\cdot2^2 - 16\cdot2 + 17 = 1$

Therefore, the vertex of the graph is $(2, 1)$. The only choice that matches this is B.

Determine the Vertex of the Graph of the Quadratic Function