Answer
See below
Work Step by Step
The standard form of the equation is: $y=ax^2+bx+c$
Given three points: $(-4,-3)\\(0,-2)\\(1,7)$
Substitute: $-3=a(-4)^2+b(-4)+c\\-2=a(0)^2+b(0)+c\\7=a(1)^2+b(1)+c$
We have the system: $16a-4b+c=-3\\c=-2\\a+b+c=7$
Substitute $c$ into the equations, we have:
$16a-4b=-1\\a+b= 9$
Multiply the second equation with $4$ and add to the first equation:
$20a=35\rightarrow a=\frac{7}{4}$
Substitute $a$ into the second equation:
$9-\frac{7}{4}=b\\
b=\frac{29}{4}$
Hence, $a=\frac{7}{4}\\b=\frac{29}{4}\\c=-2$
Substitute back to the initial equation: $y=\frac{4}{7}x^2+\frac{29}{4}x-2$
