Answer:
Step-by-step explanation:
Given quadratic function is,
f(x) = -x² - 4x + 5
Leading term of the quadratic function is 'x²'
Coefficient of this leading term is (-1).
Now we will convert this standard equation into vertex form,
f(x) = -x² - 4x + 5
= -(x² + 4x) + 5
= -[x² + 2(2x) + 4 - 4] + 5
= -[x² + 2(2x) + 2²] + 4 + 5
= -(x + 2)²+ 9
f(x) = -(x + 2)² + 9
Since, coefficient of the leading term is negative the parabola will open downwards.
Vertex form of the function is given by,
g(x) = -(x - h)² + k
(h, k) is the vertex.
By comparing the equation of the function 'g' with the function 'f',
(-2, 9) will be the vertex of the function which is the maximum point of the function.
