Help with homework(math related) How do I do this?

Question

1. Write a quadratic function that has NO x-intercepts (im sooo confused plz explain ths).

Answer 1

y=x^2 + (any number)



You know the graph y=x^2 intercepts the x-axis at (0,0). I don't know if you have learnt 'Transformations of curves'? But adding a number to the equation y=x^2 will shift the curve up by the number. For example, the equation y=x^2+5 will be the same as the original curve but will intercept the y-axis at the point (0,5) and will, therefore, not intercept/cross the x-axis at any point. It has to be a positive number because if it were negative, the curve would be moved down, meaning a part of the curve would cross the x-axis.

Hope this makes sense!

Answer 2

that mean the y value would never be 0.



so something like x^2 +1 since x^2 is always > = 0

x^2 +1 always at least 1 and never intercept x exis (that's when y = 0)