Question

What is the axis of symmetry for the graph of y-4x=7-x^2

Answer 1

as you may know, the axis of symmetry will be a coordinate off the vertex of the equation, so...


`\bf y-4x=7-x^2\implies y=7-x^2+4x\implies y=-x^2+4x+7 \\\\\\ \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llll} y = &{{ 1}}x^2&{{ +4}}x&{{ +7}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left(-\cfrac{4}{2(-1)}~~,~~7-\cfrac{4^2}{2(-1)} \right)\quad thus\implies \stackrel{\textit{axis of symmetry}}{x=~~~~-\cfrac{4}{2(-1)}}`