Question

How do find the vertex and axis of symmetry for a quadratic equation `y=-2x^2-8x+3`?

Answer 1

See the explanation below.

Explanation:

General equation for the quadratic formula: `y=ax^2+bx+c`

The graph of a quadratic equation is a parabola.The axis of symmetry is the vertical line that separates the parabola into two equal halves.The point on the x-axis where the vertical axis is placed is determined by the formula `x=(-b)/(2a)`

`y=ax^2+bx+c`

`y=-2x^2-8x+3`

`a=-2` and `b=-8`

`x=(-(-8))/(2(-2))=8/-4=-2`

`x=-2`

Substitute `-2` for `x` into the equation to find `y`.

`y=-2(-2)^2-8(-2)+3`

`y=-2(4)+16+3`

`y=-8+16+3=11`

`y=11`

The vertex of a parabola is the point where the parabola crosses its axis of symmetry. Vertex`=` `(x,y)=(-2,11)`

http://hotmath.com/hotmath_help/topics/vertex-of-a-parabola.html
http://www.mathwarehouse.com/geometry/parabola/axis-of-symmetry.php

graph{y=-2x^2-8x+3 [-16.42, 15.6, -3.2, 12.82]}