A quadratic function has a maximum point. It cuts the y axis at y = − 4 and the x axis at x = 1 and at x = 5. The x coordinate of its maximum point is:
Answers
Given : A quadratic function has a maximum point. It cuts the y axis at y = − 4 and the x axis at x = 1 and at x = 5
Solution:
A quadratic function cuts the x axis at x = 1 and at x = 5.
hence zeroes are 1 & 5
y = f(x) = a(x - 1)(x - 5)
= a(x² - 6x + 5)
cuts the y axis at y = − 4
=> a(0 - 0 + 5) = - 4
=> a = -0.8
=> y = f(x) = -0.8 (x² - 6x + 5)
= -0.8x² + 4.8x - 4
f(x) = -0.8x² + 4.8x - 4
f'(x) = -1.6x + 4.8
=> x = 3
f''(x) = - 1.6 < 0 hence f(x) is maximum at x = 3
x coordinate of its maximum point is: 3
f(x) = -0.8x² + 4.8x - 4
f(3) = -0.8(3)² + 4.8(3) - 4 =
= 3.2
Point is ( 3 , 3.2)
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