Writing Equations From Graphs...2

[nycmathguy]

Section 1.7
Question 47

See attachment.

The answer for 47a is y = -3x^2. Where did -3 come from?

The answer for 47b is 4x^2 + 3. Where did 3 and 4 come from?

 

[MathLover1]

y = -3x^2. Where did -3 come from?

In general, the parabola y=ax^2 is obtained from the basic parabola y=x^2
you are given y=ax^2 and point (1,-3)
calculate factor a
-3=a*1^2
a=-3
then equation is y=-3x^2
in your case a=-3 =>stretching parabola in the y-direction, away from the x-axis, by a factor of 3


47b is 4x^2 + 3. Where did 3 and 4 come from?

y=ax^2 +c and point (0,3)=> from this point you see that c=3
y=ax^2 +3.......you also have a point (1,7), use it to calculate factor a
7=a*1^2 +3
7-3=a
a=4
=> y=4x^2 + 3
a=4 =>stretching parabola in the y-direction, away from the x-axis, by a factor of 4

 

[nycmathguy]

y = -3x^2. Where did -3 come from?

In general, the parabola y=ax^2 is obtained from the basic parabola y=x^2
you are given y=ax^2 and point (1,-3)
calculate factor a
-3=a*1^2
a=-3
then equation is y=-3x^2
in your case a=-3 =>stretching parabola in the y-direction, away from the x-axis, by a factor of 3


47b is 4x^2 + 3. Where did 3 and 4 come from?

y=ax^2 +c and point (0,3)=> from this point you see that c=3
y=ax^2 +3.......you also have a point (1,7), use it to calculate factor a
7=a*1^2 +3
7-3=a
a=4
=> y=4x^2 + 3
a=4 =>stretching parabola in the y-direction, away from the x-axis, by a factor of 4

Thanks. I will try one more question like this one later today. Good notes.