SOLVING QUADRATIC EQUATION BY GRAPHING

Solve each equation by graphing.

Problem 1 :

y = x² -7x + 6

Solution :

Let y = x² -7x + 6

Comparing the given equation with y = ax² + bx + c, we get

a = 1, b = -7 and c = 6

x = -b/2a

x = -(-7)/2(1)

x = 3.5

When x = 3.5

y = (3.5)² -7(3.5) + 6

y = 12.25 - 24.5 + 6

y = -6.25

The vertical line drawn at x = 3.5 will divide the parabola into two parts.

The x-intercepts should be nearer to 3.5.

When x = 1, y = 1² -7(1) + 6 ==> 0

When x = 2, y = 2² -7(2) + 6 ==> -4

When x = 5, y = 5² -7(5) + 6 ==> -4

When x = 6, y = 6² -7(6) + 6 ==> 0

Problem 2 :

y = x² -10x + 25

Solution :

Let y = x² -10x + 25

Comparing the given equation with y = ax² + bx + c, we get

a = 1, b = -10 and c = 25

x = -b/2a

x = -(-10)/2(1)

x = 5

When x = 5

y = 5² - 10(5) + 25

y = 25 - 50 + 25

y = 0

The vertical line drawn at x = 5 will divide the parabola into two parts.

(5, 0) is a x-intercept. By tracing some more points.

When x = 3, y = 3² -10(3) + 25 ==> 4

When x = 4, y = 4² -10(4) + 25 ==> 1

When x = 6, y = 6² -10(6) + 25 ==> 1

When x = 7, y = 7² -10(7) + 25 ==> 4

Problem 2 :

y = x² + 3

Solution :

Let y = x² + 3

Comparing the given equation with y = ax² + bx + c, we get

a = 1, b = 0 and c = 3

Axis of symmetry is at (0, 3).

So, it is not having real roots.