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## SS2: MATHEMATICS - 2ND TERM

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Lesson 7, Topic 1
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# Graphs of Quadratic Functions

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#### 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 symmetry.
• 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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