Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x^2 + 5x – 1.

Answer 1

Answer:

The equation of the axis of symmetry is x = $-\frac{5}{8}$

The coordinates of the vertex are ( $-\frac{5}{8}$ , $-2\frac{9}{16}$ ) ⇒ 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 = $-\frac{b}{2a}$ 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 = $-\frac{b}{2a}$

∴ h = $-\frac{5}{(2)(4)}=-\frac{5}{8}$

- To find k substitute x in the function by $-\frac{5}{8}$

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

∴ k = 4 ( $\frac{25}{64}$ ) + ( $-\frac{25}{8}$ ) - 1

∴ k =  $\frac{25}{16}$  - $\frac{25}{8}$  - 1

∴ k = $-2\frac{9}{16}$

∴ The coordinates of the vertex are ( $-\frac{5}{8}$ , $-2\frac{9}{16}$ )

∵ The equation of the axis of symmetry is x = h

∵ h = $-\frac{5}{8}$

∴ The equation of the axis of symmetry is x = $-\frac{5}{8}$

Answer 2

Answer:

yo wait

Step-by-step explanation: