Question

Consider the problem of finding the line of symmetry and vertex of the quadratic equation f(x) =x^2-8x+15 What is the error in the solution below?

x^2-8x+15=0
x=-8/2 =-8/2=-4 line of symmetry
8^2-8x+15=0
 (-4)^2-8(-4)+15=0
16+32+15=0
y=63
(-4,63) vertex 



A.
The solution is correct.
B.
The line of symmetry should have been 4 instead of –4.
C.
The vertex is incorrect; it should have been {–4, 53}.
D.
-4^2 should have been squared as –16 instead of 16.

Answer 1

`\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llccll} f(x) = &{{ 1}}x^2&{{ -8}}x&{{ +15}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \textit{so the line of symmetry will be at }x=-\cfrac{{{ b}}}{2{{ a}}}`