Question

Find the vertex of a quadratic function written in standard form.

Answer 1

Answer:

our vertex for f(x) = 3x² + 18x + 32 = (-3, 5 )

Step-by-step explanation:

let me write the standard form of a quadratic equation

$a {x}^{2} + bx + c$

Now let me rewrite the original equation

$3 {x}^{2} + 18x + 32$

Now we use this simple formula to find the vertex (h, k)

$x = h = - \frac{b}{2a} \\ = - \frac{18}{2(3)} = - \frac{18}{6} = - 3 \\ h = - 3$

substitute -3 for x back into our original equation to solve for y our k value of our vertex

$y = 3 ({ - 3})^{2} + 18( - 3) + 32 \\ = 3(9) - 54 + 32 \\ = 27 + 32 - 54 \\ = 59 - 54 \\ k = 5$

our vertex for f(x) = 3x² + 18x + 32 = (-3, 5 )