Answer:
The equation of the axis of symmetry is x = [tex]-\frac{5}{8}[/tex]
The coordinates of the vertex are ( [tex]-\frac{5}{8}[/tex] , [tex]-2\frac{9}{16}[/tex] ) ⇒ 2nd answer
Step-by-step explanation:
The quadratic function y = ax² + bx + c is represented graphically by a parabola which has a minimum/maximum vertex (h , k), where
- h = [tex]-\frac{b}{2a}[/tex] and k is value y at x = h
- The axis of symmetry of the parabola is a vertical line passes through the vertex point and its equation is x = h
- The minimum/maximum value of the function is (h , k)
∵ y = 4x² + 5x - 1
∵ The form of the quadratic function is y = ax² + bx + c
∴ a = 4 , b = 5 , c = -1
∵ The coordinates of the vertex points are (h , k)
∵ h = [tex]-\frac{b}{2a}[/tex]
∴ h = [tex]-\frac{5}{(2)(4)}=-\frac{5}{8}[/tex]
- To find k substitute x in the function by [tex]-\frac{5}{8}[/tex]
∵ k = 4 ( [tex]-\frac{5}{8}[/tex] )² + 5( [tex]-\frac{5}{8}[/tex] ) - 1
∴ k = 4 ( [tex]\frac{25}{64}[/tex] ) + ( [tex]-\frac{25}{8}[/tex] ) - 1
∴ k = [tex]\frac{25}{16}[/tex] - [tex]\frac{25}{8}[/tex] - 1
∴ k = [tex]-2\frac{9}{16}[/tex]
∴ The coordinates of the vertex are ( [tex]-\frac{5}{8}[/tex] , [tex]-2\frac{9}{16}[/tex] )
∵ The equation of the axis of symmetry is x = h
∵ h = [tex]-\frac{5}{8}[/tex]
∴ The equation of the axis of symmetry is x = [tex]-\frac{5}{8}[/tex]
