I need help about vertex

Question

Which is the equation of a parabola that has the same vertex as the parabola represented by y=x², but is wider ?

Answer 1

The full formula for a parabola is y = ax²+bx+c. All that we care about in this case is a, which determines the width of the parabola and whether it opens upwards (if a is positive) or downwards (if a is negative). The smaller the absolute value of a, written as |a|, the wider the parabola. For example, y = (1/2)x² is one parabola that would be wider than the original y = x². Even wider would be y = (1/4)x².

I recommend going to the website https://www.desmos.com/calculator and plugging in the three equations to see how they compare to each other.

Answer 2

y = ax² where | a | < 1.