What is the vertex, axis of symmetry, of #y=5x^2 - 8x -6#? Does the parabola open up or down?

1 Answer
Feb 29, 2016

AOS: x= 0.8
Vertex: (0.8, -9.2)
Parabola opens: up.

Explanation:

Axis of Symmetry (vertical line that divides the parabola into two congruent halves): x= 0.8
Found by using formula: #-b/(2a)#.
(#ax^2+bx+c#, in this case b = #-8#)

Vertex (peak in the curve): (0.8, -9.2)
Can be found by imputing the Axis of Symmetry for x to find the y.
y= #5(0.8)^2-8(0.8)-6# y= -9.2

The parabola opens up since the a value of this graph is positive.
(#ax^2+bx+c#, in this case a = #5#)

You can also find all of this information by looking at it on the graph:
graph{y=5x^2-8x-6 [-8.545, 11.455, -13.24, -3.24]}