Question

enter the correct answer in the box.
the graph of a function is a parabola that has a minimum at (-1,-2) and goes through the point (0,1).
what is the equation of the function in standard form?
substitute numerical values for a, b, and c.
$y = ax^2+bx+c$

Explanation:

Step1: Use vertex form of parabola

The vertex form of a parabola with vertex $(h,k)$ is $y=a(x-h)^2+k$. Here, $h=-1$, $k=-2$, so:
$y=a(x+1)^2-2$

Step2: Solve for $a$ using point $(0,1)$

Substitute $x=0$, $y=1$ into the vertex form:
$1=a(0+1)^2-2$
$1=a-2$
$a=1+2=3$

Step3: Expand to standard form

Substitute $a=3$ into vertex form and expand:
$y=3(x+1)^2-2$
$y=3(x^2+2x+1)-2$
$y=3x^2+6x+3-2$
$y=3x^2+6x+1$

Answer:

$y=3x^2+6x+1$