Use the drop-down menus to complete the statements about the function p(x) = x(x – 1) + 1. The value of a is . The value of b is . The value of c is . The value of the discriminant is . The quadratic function will intersect the x-axis times.

Expanding the expression [tex]p(x)=x(x-1)+1 [/tex] to obtain
[tex] x^{2} -x+1[/tex]

This give the value of
a=1
b=-1
c=1

The value of discriminant is given by
[tex] b^{2}-4ac [/tex]
[tex]( -1^{2} )-4(1)(1)[/tex]=-3

The value of discriminant < 0, therefore the quadratic graph has no real roots and will cross the x-axis 0 times

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MrRoyal MrRoyal · Answer 2 · 2022-04-13T12:21:17+02:00

The function p(x) = x^2 - x + 1 is a quadratic function

The value of a is 1. The value of b is -1. The value of c is 1. The value of the discriminant is -3. The quadratic function will intersect the x-axis 0 times.

What is a quadratic function?

A quadratic function is a function that has a degree of 2

The quadratic function is given as:

p(x) = x(x - 1) + 1

Expand

p(x) = x^2 - x + 1

A quadratic function is represented as:

p(x) = ax^2 + bx + c

By comparison, we have:

a = 1, b = -1 and c = 1

The discriminant (d) is then calculated as:

d = b^2 - 4ac

So, we have:

d = (-1)^2 - 4 * 1 * 1

Evaluate

d = -3

The discriminant is less than 0.

So, the quadratic function will intersect the x-axis 0 times.

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