Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (-4,7), vertical axis of symmetry, and contains the point (2,-1). What is (a,b,c)?

Guest Sep 22, 2020

#1**+1 **

Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (-4,7), vertical axis of symmetry, and contains the point (2,-1). What is (a,b,c)?

**Hello Guest!**

\(V (-4,7)\\ P_1(2,-1)\)

Because of the symmetry around \( x = -4\), is

\(P_2(-10,-1)\)

**The coordinates of the 3 points are used in equation \(y = ax^2 + bx + c\), and the resulting equations are solved for a, b, c.**

I. \(7=16a-4b+c\)

II. \(-1=4a+2b+c\)

III. \(-1=100a-10b+c\)

III. - II. \(0=96a-12b\)

I. - II. \(8=12a-6b\)

III. - II. \(0=96a-12b\)

- 2 * (I. - II.) \(\underline{16=24a-12b}\)

\(-16=72a\)

\(a=-\frac{2}{9}\)

III. - II. \(0=96\cdot (-\frac{2}{9})-12b\\ 0=-21.\overline{3}-12b\)

\(b=-1.\overline{7}\)

III. \(-1=100a-10b+c\)

\(-1=-100\cdot \frac{2}{9} +10\cdot 1.7+c\)

\(c=3.\overline{4}\)

!

asinus Sep 22, 2020