# Thread: Parabola question.... exam ..plz help asap..

1. ## Parabola question.... exam ..plz help asap..

Write an equation of a quadratic functon that satisfies each set of condtions.

a) the function has a minimum value of 6 at x=4.

b) The parabola is congruent to y = 3x^2 and has a minimum value of 7.

the answer for part a) y = 3(x-4)^2 + 6
b) y = 3x^2+ 7

these answers are from the back of my book.. it also says that "Answers may vary"... plz help me.. .thnx

2. Originally Posted by ruscutie100
Write an equation of a quadratic functon that satisfies each set of condtions.

a) the function has a minimum value of 6 at x=4.

b) The parabola is congruent to y = 3x^2 and has a minimum value of 7.

the answer for part a) y = 3(x-4)^2 + 6
b) y = 3x^2+ 7

these answers are from the back of my book.. it also says that "Answers may vary"... plz help me.. .thnx

3. Originally Posted by ruscutie100
Write an equation of a quadratic functon that satisfies each set of condtions.

a) the function has a minimum value of 6 at x=4.

b) The parabola is congruent to y = 3x^2 and has a minimum value of 7.

the answer for part a) y = 3(x-4)^2 + 6
b) y = 3x^2+ 7

these answers are from the back of my book.. it also says that "Answers may vary"... plz help me.. .thnx
a) The (minimum) turning point is at (4, 6). You're familiar with the turning point form of a parabola - $y = a(x - h)^2 + k$ where the turning point is at (h, k) - right?

So any answer of the form $y = a(x-4)^2 + 6, \, a > 0, \,$ satisfies the given property. The book chose a = 3. Other concrete answers can be got by choosing a = 1, 2, 4, 1/2, ......

b) The turning point has y-coordinate y = 7. So k = 7 in the turning point form. In the turning point form, a 'controls the shape', so a = 3.

So any answer of the form $y = 3(x - h)^2 + 7 \,$ satisfies the given properties. The book chose h = 0, probably the simplest answer. Other concrete answers can be got by choosing h = 1, 2, 3, -1, -2 -3, 1/2, -1/2, ......

4. Originally Posted by Jhevon
That's because the answers are taken from the back of the book!

5. Originally Posted by mr fantastic
That's because the answers are taken from the back of the book!
ah, yes, i see

that's my line!

6. Originally Posted by Jhevon
[snip]

that's my line!
Ah yes. But I learnt it from you

7. Originally Posted by mr fantastic
a) The (minimum) turning point is at (4, 6). You're familiar with the turning point form of a parabola - $y = a(x - h)^2 + k$ where the turning point is at (h, k) - right?

So any answer of the form $y = a(x-4)^2 + 6, \, a > 0, \,$ satisfies the given property. The book chose a = 3. Other concrete answers can be got by choosing a = 1, 2, 4, 1/2, ......

b) The turning point has y-coordinate y = 7. So k = 7 in the turning point form. In the turning point form, a 'controls the shape', so a = 3.

So any answer of the form $y = 3(x - h)^2 + 7 \,$ satisfies the given properties. The book chose h = 0, probably the simplest answer. Other concrete answers can be got by choosing h = 1, 2, 3, -1, -2 -3, 1/2, -1/2, ......
so i can pretty much put any value for a... thnx

8. Originally Posted by ruscutie100
so i can pretty much put any value for a... thnx
Yes, as long as it's positive.