Question

Assuming all parabolas are of the form y, equals, a, x, squared, plus, b, x, plus, cy=ax
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+bx+c, drag and drop the graphs to match the appropriate a-value (if necessary).
a, equals, minus, 4a=−4 a, equals, minus, 0, point, 2, 5a=−0.25 a, equals, 0, point, 2, 5a=0.25
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Answer 1

I can’t see the graphs you’re dragging, so I’ll give the quick rule and how to use it to match each picture to an a-value. If you paste or describe each graph (orientation, narrow/wide, one or two points) I’ll match them exactly.

How to tell a from a parabola y = ax^2 + bx + c
- Sign of a: if a > 0 the parabola opens up; if a < 0 it opens down.
- Size of |a| (magnitude): larger |a| → narrower (steeper) parabola; smaller |a| → wider (flatter) parabola.
- If the vertex is at (0,0) (i.e. c = 0 and b = 0) you can compute a easily from any point (x,y): a = y / x^2.

Your given a-values:
- a = −4 : opens down and is narrow (very steep)
- a = −0.25 : opens down and is wide (shallow)
- a = 0.25 : opens up and is wide (shallow)
(If there is a fourth graph that is narrow and opens up it would be a = 4.)

Practical matching tips
- Find each graph’s direction (up or down) → separate positive vs negative a.
- Among upward-opening graphs, the narrowest is the one with the largest positive |a|; among downward-opening graphs the narrowest has the largest negative magnitude.
- If you can read a point (x,y) on the graph and you know the vertex is at the origin, compute a = y/x^2 to confirm.

If you paste the four small graph images or describe each (e.g. “opens up, passes through (1,0.25)” or “opens down, at x=1 y=−4”), I’ll assign each one to the correct a-value.