Quadratic Functions / Vertex Form / Zeros. ahh!

[Guest]

When you find the zeros in vertex form, is it the same as finding the vertex?

If not, what does finding the zeros (in a vertex form problem) mean?

 

[stapel]

Zeroes are where the quadratic (I'm assuming we're talking about a quadratic) crosses the x-axis. This will correspond to the vertex only if the vertex happens to lie exactly on the x-axis.

I don't know what your book means by "finding the zeroes in vertex form". One customarily finds the zeroes by plugging zero in for "y", and solve for x.

Eliz.

 

[Guest]

I used the quadratic formula and the answer I got was (2 + square root of 7, 2 - square root of 7)

I am not at all confident that this is correct, so if you could assure me, that would be wonderful!

 

[stapel]

Find the zeros of f (x) = 3 + 4x – x2.

The Quadratic Formula works by taking a, b, and c from "ax² + bx + c = 0". In your case, a slight rearrangement gives:

. . . . .-1x² + 4x + 3

Thus, a = -1, b = 4, and c = 3. Your solution of x = 2 ± sqrt[7] is correct.

Eliz.

 

[Guest]

Thank you so much!! That helps tons!!

But now I have another question..

In vertex form [y - 7 = a (x - h)^2]

(h, k) is the vertex and (x, y) are the points.

What does a stand for?

 

[steve_b]

But now I have another question..

In vertex form y - k = a (x - h)^2]

(h, k) is the vertex and (x, y) are the points.

What does a stand for?

=============

The a becomes the coefficient of the x^2 term, which determines two things: whether the parabola "opens up" (for a>0) or "opens down" (for a<0), and, if a is relatively small, the parabola will be "wide", while if a is relatively large, the parabola will be "narrow".

Steve