Question

cyu 4 vertex and standard form algebra 2 l identify attributes of the quadratic func 1. determine whether the function pro attributes of the quadratic function 3. $f(x)=3(x + 2)^2+8$ circle one: vertex or standard

Explanation:

Step1: Identify vertex form of quadratic

The vertex - form of a quadratic function is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex. For $f(x)=3(x + 2)^2+8$, we have $h=-2$ and $k = 8$. So the vertex is $(-2,8)$.

Step2: Determine min or max

Since $a = 3>0$, the parabola opens upward and the function has a minimum value.

Step3: Find axis of symmetry

The axis of symmetry of a quadratic function in vertex - form $y=a(x - h)^2+k$ is $x=h$. So the axis of symmetry is $x=-2$.

Step4: Calculate y - intercept

To find the y - intercept, set $x = 0$. Then $f(0)=3(0 + 2)^2+8=3\times4+8=12 + 8=20$. So the y - intercept is 20.

Step5: Determine direction of opening

Since $a=3>0$, the parabola opens upward.

Answer:

Attribute	Value
Min or Max	Min
Axis of Symmetry	$x=-2$
y - intercept	20
Direction of Opening	Upward