Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function

Answer 1

B

given the equation of a parabola in standard form

y = ax² + bx + c : a ≠ 0

then the equation of the axis of symmetry which is also the x- coordinate of the vertex is obtained using

x = - $\frac{b}{2a}$

y = 4x² + 5x - 1 is in standard form

with a = 4, b = 5 and c = - 1

$x_{vertex}$ = - $\frac{5}{8}$

hence axis of symmetry is x = - $\frac{5}{8}$

to find the y-coordinate of the vertex substitute the x-coordinate into the equation

y = 4(- $\frac{5}{8}$)² + 5(- $\frac{5}{8}$) - 1

  = $\frac{25}{16}$ - $\frac{50}{16}$ - $\frac{16}{16}$

  = - $\frac{41}{16}$ = - 2 $\frac{9}{16}$

vertex = ( - $\frac{5}{8}$, - 2 $\frac{9}{16}$)