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Solving 6x²+3=2x-6 by rewriting in standard form and identifying the parameters a, b, and c, that can be used within the quadratic formula. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Isn't the "standard form" of quadratic equations in the form, f(x) = a(x - h)2 + k? I think that I'm a little confused with the terminology here... I thought that the form that Sal was talking about here was called "general form."
• That would be vertex form.
• would standered form be considered intercept form?
• No, they are not the same. Intercept form is x/a+y/b=1 where a is the x intercept and b is the y intercept.
• I have been searching, but can not find, a video describing the process of arriving at a quadratic function. What I mean by this is for instance a question may ask one to find the function using three given points. I have seen explanations but I'm quite confident that none of them will give me as good an answer as one of Sal's videos... Help?
• The video I saw doesn't help at all. It doesn't mention anything at all about finding a quadratic equation. Could you post relevant comments, or give a URL please?
(1 vote)
• what is discriminant for? can you give an example?
D = b² - 4ac
The sign of the discriminant can be used to find the number of solutions of the corresponding quadratic equation. There are 3 cases:
• If D > 0, we have two solutions.
• If D = 0, we have only one solution.
• If D < 0, we have no (real) solutions.
Ex.) How many solutions does the equation x² - 5x + 2 = 0 have?
a = 1, b = -5, c = 2
D = (-5)² - 4 * 1 * 2 = 17
Because D > 0, we have two solutions.
• According to my poorly written precalculus textbook, f(x)=(ax^2)+bx+c is not the standard form of a quadratic equation; it's called general/common form. My textbook defines standard form as being written f(x)= (a(x-h)^2)+k where h and k can be taken as the vertex of the parabola. I also can't seem to find this h-k form of quadratic equations anywhere on this site. It also says this h-k form can be reached from completing the square, but i can't relate the completing the square video to h-k form.
• I'm looking for standard form ax+by=c.
• that is the standard form of linear equations
• For standard form of a quadratic, does the leading coefficient (the a term) have to be positive?
• A positive leading coefficient creates a graph that opens upward, and a negative leading coefficient will open downward
• Is
-1 ± √41
_______
-6

equivalent to

1 ± √41
_______
6

?
And if so, wouldn't the second example be 'more' simplified as it removes unnecessary negation?
(1 vote)
• Yes, they are equivalent. And, yes the 2nd version is more simplfied.

Sum of 2 natural number is 8 and the difference of their reciprocal is 2/15. Find the nuumbers using one variable.
(1 vote)
• x = one number
8-x = 2nd number
The reciprocal of x = 1/x
The reciprocal of 8-x = 1/(8-x)
The difference of their reciprocals becomes: 1/x - 1/(8-x) = 2/15
Then solve the equation.
See if you can find the 2 numbers. Comment back if you get stuck. Let me know what you tried to do.