By examining the sign ofthe discriminant in part a how many x-intercepts would the graph of y=x^2 +x+3 have?

Answer 1

discriminant is b^2 - 4ac which for your problem a = 1 b = 1 and c = 3

b^2 - 4ac = 1^2 - 4(1)(3) = 1 - 12 = -11
since it is a negative, then there are NO x-intercepts as the solutions for y = 0 will be imaginary

Answer 2

To find the discriminant you must first use the quadratic formula which is:
A = (-b + or - sqrt(b^2 - 4ac))/2a

As we only need the discrimant we look at the part in the second set of brackets
b^2 - 4ac
So if we substitute our numbers (a = 1 b = 1 c = 3) we get
1 - 12 = -11
As the discriminant is a negative number the line has no real roots therefore it will not intercept the x axis.

Answer 3

Discriminant = b^2 - 4ac

If the discriminant is greater than 0, there will be 2 real roots, hence 2 x-intercepts.
If the discriminant is less than 0, there will be 2 imaginary roots or no real roots, hence 0 x-intercepts.
If the discriminant is equal to 0, there will be 1 real root, hence 1 x-intercepts.

In y=x^2 +x+3, the discriminant is (1^2) - 4(1)(3) = -11 < 0
Hence it has no x-intercepts.

Answer 4

well...if you make x = 0 and look at the y intercept...you will notice it will be y = 3

so then if you were to look at the sign of the x, it's positive...that means the function will be concave up (it will be in the shape of a bowl) and so the function will never go below y = 3

thus, there are no x intercepts

Answer 5

a=1,b=1c=3
b^2-4ac=1-12=-11
when discriminant is neg, there is no real root, so there is no x-intercept