Question

The function f(x) = − x^2+ bx +1 is shown in the graph. What is the value of b?

Answer 1

b = 4

Explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here ( h, k ) = (2, 5 ) , then

y = a(x - 2)² + 5

to find a substitute any point on the parabola into the equation

using (0, 1 ) then

1 = a(0 - 2)² + 5 ( subtract 5 from both sides )

- 4= a(- 2)²= 4a ( divide both sides by 4 )

- 1 = a

then

y = - ( x - 2)² + 5

= - (x² - 4x + 4) + 5

= - x² + 4x - 4 + 5

= - x² + 4x + 1 ← in the form ax² + bx + c

with b = 4