Thread: Turning Point of a Parabola

Hello,

How do I find the turning point of a parabola?

Thanks in advance

Originally Posted by J4553

Hello,

How do I find the turning point of a parabola?

Thanks in advance

Complete the square.

Alternatively, use calculus.

Post a more specific question (and state your mathematical background).

Originally Posted by J4553

Hello,

How do I find the turning point of a parabola?

Thanks in advance

The turning point of a parabola is the vertex of the parabola.

For the given equation of parabola, you can find the vertex by completing the square in the form



where (h, k) is vertex.

If, suppose equation of a parabola is



Then, complete the square, so, eqn becomes,



so, vertex = (1, 2)

so, turning point = (1, 2)

Did you get it now???

Shyam - no, I'm afraid that just confuses me even more.
I think my lecturer gave the formula: -b/2a to find the x-component of the vertex, then may have said to substitute that value into another equation to find the y-component.
Does this sound right or am I way off?

Originally Posted by J4553

Shyam - no, I'm afraid that just confuses me even more.
I think my lecturer gave the formula: -b/2a to find the x-component of the vertex, then may have said to substitute that value into another equation to find the y-component.
Does this sound right or am I way off?

that formula is correct, for example, take this function;

y=x^2+6x+8

b=6, a=1

-b/2a=-6/2(1)=-3

sub -3 into the function to get the value of y

y=(-3)^2+6(-3)+8=-1

therefore, the vertex for this example is (-3,-1)

Shyam is simply using another method then the one you are instructed to use

Perfect - thanks!

Originally Posted by J4553

Shyam - no, I'm afraid that just confuses me even more.
I think my lecturer gave the formula: -b/2a to find the x-component of the vertex, then may have said to substitute that value into another equation to find the y-component.
Does this sound right or am I way off?

Yes, your formula is correct.

If, suppose equation of a parabola is







y = 2

so, you have (1, 2) as the vertex or turning point of parabola