Topic Content:
- Graphs of Quadratic Functions
The expression x2 + bx + c is called a quadratic function of x, where a, b and c are constants. When a quadratic function y = x2 + 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 T1 and T2 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 ymin is at the turning point T1 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 ymax is at the turning point T2 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 = x2 + 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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