Question

assuming all parabolas are of the form y = ax^2 + bx + c drag and drop the graphs to match the appropriate a-value

Answer 1

A parabola has the form:

y = a*x^2 + b*x + c

Where a is the leading coefficient.

If a is positive, the parabola opens up.

If a is negative, the parabola opens down.

a is the factor that multiplies the part that grows the fastest in the equation, thus, if a is a larger value (in absolute value) then the parabola will grow faster (then the parabola will be narrow)

if a is smaller (again, in absolute value) the parabola will grow slower, then the parabola will be wider.

With this, we can conclude that:

a = -4

is the largest value of a in absolute value.

Then this corresponds to the thinner parabola (the one at the left)

a = -1

Is the middle value of a, then this corresponds to the graph of the middle

a = -0.25

Is the smallest absolute value of a, then this one corresponds to the widest graph (the first one at the left)