F.4 QUADRATIC FUNCTIONS(GRAPH)

y = y=bx^2 + cx +a where c = 0 , a and b are negative

The graph looks like this:
y
|
|
|
-------|--------- x
|
|
*
* | *
* | *
* | *

Note: * are points on the curve.
The vertex is (0, a) where a is negative This is a maximum point.
The y-intercept is a. There are no x-intercepts.
The line of symmetry is the y-axis.
The parabola lies below the x-axis.

Since c is zero, the quadratic function is reduced to y = bx^2 + a
Since b is negative, it involves a reflection in the x-axis. The parabola opens down. That means the graph shows a maximum point. The vertex is at (0, a) where a is negative value. y can never have a value greater than a.

There is vertical translation of |a| units. Since a is negative, the whole curve moves down by |a| units when comparing to y = -x^2.

The graph can be stretched down vertically if |b| is greater than 1 (more pointed) or compressed up vertically if |b| is less than 1 (more flatter).

For example:
y = -2x^2 – 3 (the curve is more pointed)
y = -0.5x^2 – 3 (the curve is more flatter)