Question

What is the axis of symmetry for f(x)=- 3x^ 2 +18x-7?
X=-3
X=3
X=-6
X=6

Answer 1

this is a quadratic equation with a squared "x" variable, and therefore a vertical parabolic graph, and thus, the axis of symmetry will be from the vertex's x-coordinate, hmmmm what is its vertex coordiinate anyway?


`\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-3}x^2\stackrel{\stackrel{b}{\downarrow }}{+18}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{18}{2(-3)}~~,~~\qquad \right)\implies \left( +\cfrac{18}{6}~~,~~\qquad \right)\implies (3~,\quad ) \\\\\\ \stackrel{\textit{axis of symmetry}}{x=3}`

Answer 2

The axis of symmetry is a vertical line through the vertex.

The vertex is at


`x=-b/2a=-18/(2(-3))=3`

Second choice.