Question

Write an equation(any form) for the quadratic graphed below:

Answer 1

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

Explanation:

The equation for a quadratic graph can be expressed in the Vertex form:

`y = a(x-h)^(2) + k`

Where:

`(h, k)` = Vertex of the parabola

= Extreme point of the parabola

Step I:
By reading from the graph:

`(h, k)` =
`(-3, 3)`

Substitute the values of h and k in the above equation:

`y = a[x- (-3)]^(2) + (3)`

`y = a(x + 3)^(2) + 3`

Step II:

Determine a:

Based on the shape of the graph (which is an upside down U), the value of a will be negative:

Count one unit to the right from the vertex and see how far do you go down to touch the graph:

From the graph:

It seems you need to move 2 units down

∴a =
`-2`

Step III:
Substitute this value of a in the above equation:

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