How do I find the x coordinate of the vertex of the parabola defined by the function f(x)=-7x^2+9x+4

Question

mathmale · Answer

There's a formula that stems from the quadratic formula that will enable you to find the x-coordinate of the vertex of your parabola quickly.

Mind typing or drawing the quadratic formula here?

anonymous · Answer

is it f(-b/2a)?

mathmale · Answer

that's not the quadratic formula, although that -b/(2a) does come from the quadratic formula.  Mind trying once more...looking up the formula if need be...?  What is the quadratic formula?

anonymous · Answer

ax^2+bx+c=0?

mathmale · Answer

Have you actually looked up "quadratic formula" on the Internet or in your online learning materials or in a textbook?  $$ax^2+bx+c=0$$ is a quadratic equation; it is not the quadratic formula.

anonymous · Answer

@mathmale  the questions asks for the first coordinate of the  vertex, not the zeros
in fact the first coordinate of the vertex is $-\frac{b}{2a}$

anonymous · Answer

in this case $a=-7,b=9$

mathmale · Answer

@satellite73:  I am fully aware of that.  We need a formula for the x-coordinate of the vertex, which just so happens to be part of the quadratic formula.  I was asking @cazzrock02 for the quadratic formula as a way of determining what he / she knows about this topic.

anonymous · Answer

not to be argumentative, but if someone is looking for the first coordinate of the vertex $-\frac{b}{2a}$ what is the point of 

"Have you actually looked up "quadratic formula" on the Internet or in your online learning materials or in a textbook? "

anonymous · Answer

I am mainly lost with this.  Thank you satellite73

mathmale · Answer

As you can see from the above conversation, cazzrock02 was unable to produce the quadratic formula.  

All right, cazzrock02:  the quadratic formula is $$x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }$$

mathmale · Answer

You'll notice that if you take only the first part, $$x=\frac{ -b }{ 2a },$$

mathmale · Answer

... we have precisely the formula we need for the x-coordinate of the vertex.

In my opinion it's easier to know ONE formula, the quadratic formula, rather than TWO formulas, the quadratic formula and that for the x-coordinate of the vertex.

mathmale · Answer

And I would expect that both formulas would be mentioned at about the same time in any algebra course, and would venture that expecting an algebra student to know the quadratic formula is not asking too much.

mathmale · Answer

If$$f(x)=-7x^2+9x+4,$$what are the coefficients a, b and c?

In other words, find the values of a, b and c from the given formula.  @cazzrock02?

mathmale · Answer

Compare these two:$$f(x)=-7x^2+9x+4$$

mathmale · Answer

and$$f(x)=ax^2+bx+c$$   Here the coefficients of x^2 are -7 and a.  Therefore, a=-7.
Here the coefficients of x are 9 and b.  Hence, b=9.  c=4, using the same reasoning.

Thus, as satellite73 pointed out to you earlier, a=-7 and b=9.

Evaluate $$x=\frac{ -b }{ 2a }$$now, please.  If you do that correctly, you'll have the answer to this problem.