Finding the constant. (1 Viewer)

[Psychosomatical]

Doing past trial papers is fun...

"A parabola is concave up, has an axis of symmetry at x = -2 and a horizontal tangent at y = -3. When the equation of the parabola is expressed in the form of y = ax^2 + bx + c. the value of a is one.

Determine the equation of the parabola and show that this parabola has two irrational roots."

Ok so i know that I can use the axis of symmetry formula to find b (-b/2a = -2 ) therefore b = 4. So i am left with x^2 + 4x + C.. How can i find the constant. Must i sub something into the discriminant formula.. or use what info i have available.. pretty sure i'm missing something here. bare with me

Any help would be appreciated. Thanks.

 

[kaz1]

Doing past trial papers is fun...

"A parabola is concave up, has an axis of symmetry at x = -2 and a horizontal tangent at x = -3. When the equation of the parabola is expressed in the form of y = ax^2 + bx + c. the value of a is one.

Determine the equation of the parabola and show that this parabola has two irrational roots."

Ok so i know that I can use the axis of symmetry formula to find b (-b/2a = -2 ) therefore b = 4. So i am left with x^2 + 4x + C.. How can i find the constant. Must i sub something into the discriminant formula.. or use what info i have available.. pretty sure i'm missing something here. bare with me

Any help would be appreciated. Thanks.

wtf? Aren't those supposed to be the same thing on a parabola?

 

[Psychosomatical]

wtf? Aren't those supposed to be the same thing on a parabola?

I apologise, all fixed. meant to be y.

 

[jet]

 

[Psychosomatical]

Ahh ok so in effect we are solving them simultaneously as both pass through teh same point, thus making them equal one another to solve for C... ? maybe.

Thankyou very much

 

[Drongoski]

I apologise, all fixed. meant to be y.

In that case question is easy.

The eqn of the parabola is of form: y-k = 1(x-h)² where (h,k) =(-2,-3)

i.e. y-(-3) = 1(x-(-2))²

i.e. y+3 = x²+4x+4

i.e. y = x² + 4x +1

.: discriminant = "b^2-4ac" = 16-4 = 12 and its square root = +- 2 sqrt(3)

.: the eqn: x²+4x+1 = 0 has 2 distinct and irrational roots (whatever they are)

 

[Psychosomatical]

In that case question is easy.

The eqn of the parabola is of form: y-k = 1(x-h)² where (h,k) =(-2,-3)

i.e. y-(-3) = 1(x-(-2))²

i.e. y+3 = x²+4x+4

i.e. y = x² + 4x +1

.: discriminant = "b^2-4ac" = 16-4 = 12 and its square root = +- 2 sqrt(3)

.: the eqn: x²+4x+1 = 0 has 2 distinct and irrational roots (whatever they are)

Thank you very much.