What is the equation for the line of symmetry for the graph of the function y=-4x^2+6x-8?

2 Answers
Jun 7, 2016

The axis of symmetry is the line x = 3/4

Explanation:

The standard form for the equation of a parabola is

y = ax^2 + bx + c

The line of symmetry for a parabola is a vertical line. It can be found by using the formula x = (-b)/(2a)

In y = -4x^2 + 6x -8, " "a = -4, b= 6 and c = -8
Substitute b and c to get:

x = (-6)/(2(-4)) = (-6)/(-8) = 3/4

The axis of symmetry is the line x = 3/4

Jun 7, 2016

x = 3/4

Explanation:

A parabola such as

y = a_2x^2+a_1x+a_0

can be put in the so called line of symmetry form by
choosing c,x_0, y_0 such that

y = a_2x^2+a_1x+a_0 equiv c(x-x_0)^2+y_0

where x = x_0 is the line of symmetry. Comparing coefficients we have

{ (a_0 - c x_0^2 - y_0 = 0), (a_1 + 2 c x_0 = 0), (a_2 - c = 0) :}

solving for c, x_0, y_0

{ (c = a_2), (x_0 = -a_1/(2 a_2)),( y_0 = (-a_1^2 + 4 a_0 a_2)/(4 a_2)) :}

In the present case we have c = -4, x_0 = 3/4, y_0 =-23/4 then

x = 3/4 is the symmetry line and in symmetry form we have

y = -4(x-3/4)^2-23/4