Question

How do you tell whether the graph opens up or down, find the vertex, and find the axis of symmetry given `y=-2x^2-6x+3`?

Answer 1

Opens Down
Vertex: (-`3/2`, `15/2`)
Axis of Symmetry: x=-`3/2`

Explanation:

So one of the easiest ways you can find this information is by graphing. The axis of symmetry will always be a vertical line for a quadratic equation, so it will always be x= (x value of the vertex)

Let's start from the basics,

Standard form, a`x^2`+bx+c

The a value determines whether the parabola is face up or down. A negative 'a' value, such as -2, makes the parabola open down, whereas a positive 'a' value like 2, will make the parabola open up.

To find the vertex of a quadratic function, first calculate `(-b)/(2a)` to find the 'x' value of the vertex.

So `(-(-6))/(2(-2))`, gives you `-3/2`. This is the x value of the vertex. And you can then determine the axis of symmetry from here which is x= `-3/2`

Now for the 'y' value of the vertex, simply substitue `x` with `-3/2` and solve.

So, -2 `(-3/2)^2`-6(`-3/2`)+3

This simplified gives you -`9/2`+ 9 + 3
Add the numbers together, and you should get `15/2`

So your vertex is (-`3/2`, `15/2`)

Hope this clarifies things!