The maximum value of a quadratic function f is −3, its axis of symmetry is x=2 and the value of the quadratic function at x=0 is −9. What will be the coefficient of x2 in the expression of f? About the author Mary
Given : The maximum value of a quadratic function is – 3 its axis of symmetry is x = 2 value of the quadratic function at x = 0 is – 9 To Find : the coefficient of x² Solution: axis of symmetry is x = 2 => f(x) = a(x – 2)² + c f’ (x) = 2a(x – 2) f’ (x) = 0 => x = 2 f”(x) = 2a < 0 because its maximum value Hence a is -ve f(2) = -3 => -3 = a(2 – 2)² + c => -3 = c Hence f(x) = a(x – 2)² – 3 value of the quadratic function at x = 0 is – 9 => f(0) = – 9 => -9 = a( 0 – 2)² – 3 => -6 = 4a => a = -6/4 => a = – 3/2 f(x) =(-3/2)(x – 2)² – 3 = (-3/2)(x² -4x + 4) – 3 = (-3/2)x² + 6x – 6 – 3 = (-3/2)x² + 6x -9 coefficient of x² = -3/2 Learn More: Vertex A (4, –5) and point of intersection O (–6, 7) of diagonals of … brainly.in/question/12195097 A point where two sides of triangle meet is known as – of a triangle … brainly.in/question/6135034 Reply
Answer:
it is so difficult i think and ia am a kid
Given : The maximum value of a quadratic function is – 3
its axis of symmetry is x = 2
value of the quadratic function at x = 0 is – 9
To Find : the coefficient of x²
Solution:
axis of symmetry is x = 2
=> f(x) = a(x – 2)² + c
f’ (x) = 2a(x – 2)
f’ (x) = 0 => x = 2
f”(x) = 2a < 0 because its maximum value
Hence a is -ve
f(2) = -3
=> -3 = a(2 – 2)² + c
=> -3 = c
Hence f(x) = a(x – 2)² – 3
value of the quadratic function at x = 0 is – 9
=> f(0) = – 9
=> -9 = a( 0 – 2)² – 3
=> -6 = 4a
=> a = -6/4
=> a = – 3/2
f(x) =(-3/2)(x – 2)² – 3
= (-3/2)(x² -4x + 4) – 3
= (-3/2)x² + 6x – 6 – 3
= (-3/2)x² + 6x -9
coefficient of x² = -3/2
Learn More:
Vertex A (4, –5) and point of intersection O (–6, 7) of diagonals of …
brainly.in/question/12195097
A point where two sides of triangle meet is known as – of a triangle …
brainly.in/question/6135034