How would you find the vertex of this quadratic function either by finding the vertex using a, b, and c or finding the vertex by using just a and b?

Question

comm.dan · Answer

To find using a, b, and c, you use the Quadratic Formula.
To find using a and b you use x equals negative b over 2a, then you put the x back into the original quadratic function to find the y.

comm.dan · Answer

Here is the problem y equals -x squared + 1/2x + 2

comm.dan · Answer

The Quadratic Formula is x equals -b + or - square root sign then b squared -4ac over 2a

amistre64 · Answer

the vertex is along the x = -b/(2a) axis

therefore the vertex itself is simply (-b/(2a), f(-b/(2a)))

amistre64 · Answer

$$y = (-x)^2 + \frac{1}{2x} + 2$$
what is your equation?

comm.dan · Answer

The equation is y equals -x squared + 1/2x + 2

comm.dan · Answer

@amistre64

harsimran_hs4 · Answer

are you trough with the question or still some confusion?

amistre64 · Answer

youre restating the equation in the same manner that you first presented it does not clarify it in any way whatsoever ...

comm.dan · Answer

I get how to get the first answer but not the second answer @amistre64 and @harsimran_hs4

amistre64 · Answer

the structure of the quadratic formula informs us about the axis of symmetry (the middle of the parabola) as well as the x intercepts (which are equal distances to the left and right of the axis of symmetry).  All these parts reflect the value of the x components of the parabola.

$$\left(\frac{-\sqrt{b^2-4ac}}{2a}\right)\leftarrow\leftarrow \left(\frac{-b}{2a}\right)\to \to\left(\frac{+\sqrt{b^2-4ac}}{2a}\right)$$

Since the vertex of the parabola lies on the axis of symmetry, the value of the x component of the vertex is: $\Large \frac{-b}{2a}$ .  Can you see what happens to the left and right parts of this?  If $b^2-4ac$ is a positive value; we have 2 equal distances from the center that define the x intercepts.  If $b^2-4ac$ is equal to 0, then we only have one point on the x axis, the vertex itself.  If $b^2-4ac$ is a negative value, then there is no points of the parabola touching the x axis and therefore it is floating someplace above or below it.