#### Topic Content:

- Graphs of Quadratic Functions

The expression x^{2} + bx + c is called a quadratic function of x, where a, b and c are constants. When a quadratic function y = x^{2} + bx + c is plotted, its graph gives a smooth curve called a parabola.

Consider \( \scriptsize y = x^2 + bx + c\)

Also, we can have Consider \( \scriptsize y = -ax^2 + bx + c\)

**Hint: **The highest power of x is 2 i.e. a second degree function

- The points T
_{1}and T_{2}are the turning points i.e. where the curve changes direction (inflexion point) - When a is positive, we have a minimum curve with shape and the minimum value of the function y
_{min}is at the turning point T_{1}and the value of x where it occurs gives the equation of the line of symmetryA line of symmetry is the line that divides a shape or an object into two equal and symmetrical parts. More. - When a is negative, we have a maximum curve shape and the maximum value of the function y
_{max}is at the turning point T_{2}and the value of x where it occurs gives the equation of the line of symmetry. - The line of symmetry or the axis of symmetry divides the curve into two equal parts.

### Example 7.1.1:

Plot the curve of y = x^{2} + x – 6 for values of x from -4 to 3**(a)** Use the curve to find :

(i) the values of x when y = 2.8

(ii) the value of y when x = 1.4

(iii) the minimum value of the function and the value of x**(b) **Draw the axis of symmetry of the curve and write down its equation

**Solution:**

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