Question

the quadratic curve crosses the x axis at 1,0 and 5,0 and the y intercept is 5. express this in the equation y = ax2 + bx + c

Answer 1

• y = x² - 6x + 5

Explanation:

As per question there are 3 points on the curve:

• (1, 0), (5, 0) and (0, 5)

Substitute the x- and y- values into equation and find the values of a, b and c.

x = 0, y = 5

• 5 = a*0² + b*0 + c
• 5 = c
• c = 5

x = 1, y = 0

• 0 = a*1² + b*1 + 5
• a + b = - 5 (1)

x = 5, y = 0

• 0 = a*5² + b*5 + 5
• 25a + 5b = - 5
• 5a + b = - 1 (2)

Subtract the equations 1 and 2:

• 5a - a + b - b = - 1 - (- 5)
• 4a = 4
• a = 1

Now find the value of b:

• 1 + b = - 5
• b = - 5 - 1
• b = - 6

The equation of the curve is:

• y = x² - 6x + 5