Question

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

Answer 1

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]}