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)?
+15001 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. \(-1=100a-10b+c\)
\(-1=-100\cdot \frac{2}{9} +10\cdot 1.7+c\)
\(c=3.\overline{4}\)
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