Question

3
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

Vertex form: $y = a(x - h)^2 + k$, where $(h,k)=(-1,-2)$. So $y = a(x + 1)^2 - 2$.

Step2: Find a using (0,1)

Substitute $x=0,y=1$: $1 = a(0 + 1)^2 - 2 \Rightarrow a = 3$.

Step3: Expand to standard form

$y = 3(x^2 + 2x + 1) - 2 = 3x^2 + 6x + 3 - 2 = 3x^2 + 6x + 1$.

Step4: Identify a,b,c

$a=3$, $b=6$, $c=1$.

(Note: The final equation in standard form is $y = 3x^2 + 6x + 1$.)

Answer:

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