# Sketching a graph of Quadratic function

The curve has a minimum value at y = –12.4 and x = –2.3. So the
coordinates of the vertex is (–2.3, –12.4).
From the graph, the curve cuts the x–axis at two distinct points, i.e. at
–6 and 1. At these points, the y–coordinates are zero.

so far from

Therefore X =-6 and x= 1 are the solutions to the quadrantic equation above.

This implies that we can also use graphical mean to solve a given quadratic equation.

Example

Draw the graph of

for values of x from -2 to 4. Find the graph find

a). The minumum of

b)The value of x for which y is greatest, hence state the coordinates of the vertex (maximum point).

c) the range of values of x for which y is positive.

Solution

From the graph:

The maximum value of

b) The value of x for which y is greatest is 1. Hence the coordinates of vertex is (1, 3).

c) The curve cuts the x–axis at x – 0.8 and, x 2.8 . Therefore, y is positive for all parts of the curve above the x–axis i.e. when x >-0.8 and, x <2.8. In other words, y is positive over the range – 0.8< x <2.8