Question

tentukan fungsi kuadrat yang grafiknya memotong sumbu -x pada titik koordinat (4,0) dan (-3,0) serta malalui titik koordinat (2,-10)

Answer 1

Answer:

x² - x  - 12

Step-by-step explanation:

Determine the quadratic function whose graph intersects the x-axis at the coordinates (4.0) and (-3.0) and through the coordinates (2, -10)

f(x)  = ax²  + bx  + c

f(4) = 0

=> a(4)² + 4b + c = 0

=> 16a + 4b + c = 0

f(-3) = 0

=> a(-3)² -3b + c = 0

=> 9a -3b + c = 0

16a + 4b + c = 9a -3b + c

=> 7a = -7b

=> a = - b  or b = -a

f(x) = ax² - ax + c

f(2) = -10

=> a(2)² - 2a + c = -10

=> 4a - 2a +c = -10

=> 2a + c=  -10

9a -3b + c = 0

=> 9a + 3a + c = 0

=> 12a + c = 0

10a = 10

=> a = 1

c = -12

f(x) = x² - x  - 12

other way to solve , as it cut x -axis at 4 & - 3

=>  (x - 4)(x -(-3)) = 0

=> (x - 4)(x + 3) = 0

=> x² - 4x + 3x - 12 = 0

=> x² - x - 12 = 0

=> f(x) =  x² - x - 12