Question

function provided is written in standard or vertex form. rewrite the function using the form provided.

1. $f(x)=9x^{2}+18x + 14$

circle one: vertex or standard
vertex
min or max
axis of symmetry
y - intercept
direction of opening

Explanation:

Step1: Identify the form

The function $f(x)=9x^{2}+18x + 14$ is in standard form $y = ax^{2}+bx + c$ where $a = 9$, $b=18$, $c = 14$. Circle: Standard.

Step2: Convert to vertex - form

Complete the square. $y=9x^{2}+18x + 14=9(x^{2}+2x)+14$.
Inside the parentheses, $(x^{2}+2x)=(x + 1)^{2}-1$. So $y=9((x + 1)^{2}-1)+14=9(x + 1)^{2}-9 + 14=9(x+1)^{2}+5$. The vertex is $(-1,5)$.

Step3: Determine min/max

Since $a = 9>0$, the parabola opens upward, so it has a minimum. Min.

Step4: Find axis of symmetry

For a parabola in the form $y=a(x - h)^{2}+k$, the axis of symmetry is $x = h$. Here $h=-1$, so the axis of symmetry is $x=-1$.

Step5: Find y - intercept

Set $x = 0$ in the original function. $y=9(0)^{2}+18(0)+14=14$.

Step6: Determine direction of opening

Since $a = 9>0$, the direction of opening is upward.

Answer:

Property	Value
Min or Max	Min
Axis of Symmetry	$x=-1$
y - intercept	$14$
Direction of Opening	Upward