Quadratic equations and Quadratic graphs

Roots of a Quadratic Equation
Definition of Roots of a Quadratic Equation

• The solutions of a quadratic equation are called the roots of a quadratic equation.

Example on Roots of a Quadratic Equation

• The solutions or the roots of the quadratic equation x² - x - 2 are 2 and - 1.

1. We find the coordinates of X and Y on the graph by naming one of them = 0

2. When the graph of y = ax ^2 + bx + c touches the x-axis at one point, we cant say that the roots of the equation is repeated.

3. When the graph of y = ax ^2 + bx + c does not touche the x-axis at one point, we cant say that the equation has no real roots.

Also, students please remember to write down the specifics for one's own graph like writing 1cm= to represent 2 units!

Methods to solve quadratic equations

1 . Solving the quadratic equations by factorization
Students must aim to write the quadratic equation in the general form and put all terms on one side and 0 on the other side before factorizing.

2. Solving the quadratic equations by completing the square

For example. ( x-3 ) ^2 = 25
x-3 = plus, minus 25
x-3 = plus minus 5
hence , x-3= 5 or x-3 = -5

Tips for quadratic equations solving.

1. Always express the quadratic equation in the general form
2. When applying to some questions , we might have some rejected answers like negative answers when they asking for length.

When solving, we can recall the rules we learnt earlier.

Gradient of a Straight Line

1. The gradient of a straight line is the measure of its steepness of the slope
2. The gradient is the ratio of the vertical distance.

Remember ! gradient = Rise/ Run

3. To find the gradient m , of the line passing through 2 points, A ( x1, x2 ) and B ( X2, Y2 )
Use the formula Gradient m , = y2-y1 / x2-x1.

Y= mx + c
m= gradient while
c = y intercept

Line of intercept = The middle, commonly the minimum or the maximum point !
Also another tip: Always remember to draw the graph enlarged so that the points is clearly shown