To calculate: The x and y intercept of the function g(x)=−x2+x−1

Question

To calculate: The x and y intercept of the function   g(x)=−x2+x−1

Warajected53 · Accepted Answer

Step 1
Formula used:
For a quadratic equation of the form

a x^{2} + b x + c = 0 (a \neq 0)

the discriminant is

b^{2} - 4 a c

For a quadratic equation of the form

a x^{2} + b x + c = 0

the solutions are:

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Step 2
Consider the provided function:

g (x) = - x^{2} + x - 1

As it can observed that the provided functions a quadratic equation and for a quadratic equation of the form

a x^{2} + b x + c = 0 (a \neq 0)

the discriminant is

b^{2} - 4 a c

Thus, the discriminant for the provided equation will be obtained by substituting -1 for a, 1 for b and -1 for c in the formula of discriminant as:

b^{2} - 4 a c = {(1)}^{2} - 4 (- 1) (- 1)

= 1 - 4

= - 3

Since,

- 3 < 0

, so there will be no x-intercepts.
To find y-intercept, evalue

g (0)

as:

g (0) = - {(0)}^{2} + (0) - 1

= - 1

Thus, the y-intercept is

(0, - 1)

The corresponding graph of

f (x)

is provided for better illustration:

To calculate: The x and y intercept of the function g(x)=-x^{2}+x-1