Question

Fill in the blanks concerning the following quadratic function: f(x)=−x2−4x+5

.

The leading coefficient of f(x)
is

Answer 1

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.