Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x^2-8x-3

Answer 1

x = 1 and vertex = (1, - 7 )

Explanation:

Given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 )

The the equation of the axis of symmetry which is also the x- coordinate of the vertex is

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

y = 4x² - 8x - 3 ← is in standard form

with a = 4, b = - 8 , then

x = -
`(-8)/(8)` = 1

That is equation of axis of symmetry is x = 1

Substitute x = 1 into the function for y- coordinate of vertex

y = 4(1)² - 8(1) - 3 = 4 - 8 - 3 = - 7

vertex = (1, - 7 )