Can someone tell me what the co-effecients on a Quadratic Equation actually mean?

Question

I have the quadratic equation y = 0.0654x^2 + 1.9506x + 896.2, but which part is what? Which part is the intercept, slope, etc? Thanks!

Answer 1

The only equations that have slope and intercept are linear equations of degree one. These all look like:

y = ax + b

A quadratic equation looks like:

y = ax² + bx + c

Quadratic equations do not have a constant slope, so you can't just read it off of the equation.

In fact (and this is from calculus, so don't worry if you don't understand), the slope of a quadratic equation is given by:

slope = 2ax + b

(where a is the coefficient of x² and b is the coefficient of x in the original polynomial).

Most of the time, people don't care about the y-intercept of a quadratic equation, because it doesn't really help with the graph. If you need it, though, it would be the value of the function where x = 0. That would just be:

y-intercept = a(0)² + b(0) + c = c

More often in graphing quadratic equations, you're interested in the x-intercepts. Those are the values where the answer that you get when you plug in x is 0.

ax² + bx + c = 0

To find the x-intercepts, you can use FOIL, complete the square, or the quadratic formula. (There may be 0, 1, or 2 x-intercepts.)

Answer 2

A quadratic equation is one in the form ax^2 +bx +c =0
What you have is a quadratic function, the kind of thing you use to draw a graph. The intercept you would be likely to want is the x intercept, which means the value of x when y =0. In a quadratic there are likely to be two values of x when y=0. The slope keeps changing as it is a curved graph. If you need the slope at a particular point you should do A level maths.

Answer 3

Jim's answer was great. If you didn't understand some parts, here is a little summary focused on your question:

When you mentioned "slope" and "y-intercept", you really are talking about lines. Example:

f(x) = 3x - 5

I'm sure you have seen those before. The y-intercept is -5, and the slope is 3, and you can graph that easily.

The coefficients in this case are also 3, and -5. When we talk about coefficients, sometimes the most important coefficient is the "leading coefficient". In the example I gave, the leading coefficient is 3.

If you have:

f(x) = 2x + 4x^2 - 10

It is best to rewrite in standard form (highest exponent to lowest)

f(x) = 4x^2 + 2x - 10

And the leading coefficient is 4. The other coefficients are 2 and -10.

Both of these examples (and your problem) are functions called polynomials.

In a polynomial, the leading coefficient gives us information. In the first example, it gave us slope. In the second example, it isn't as specific, but it does give us some information as to the shape of the graph. I won't go into the details here...your teacher will anyways.

Hope this helped a little. Open your math book, look up "polynomial" in the index, and read a little about it!

Answer 4

the slope of the quadratic
y = 0.0654x^2 + 1.9506x + 896.2
is 0.1308x+1.9506 which is a straight
line
the coefficients are
0.0654 for the x^2
and 1.9506 for the x
the constant is 896.2
the y intercept is on the y axis(ie when
x=0) and in this case is 896.2

the x intercept(s) is when y=0 (ie on the
x axis)

in a normal quadratic,
ax^2+bx+c=0,there are 0,1 or 2
x intercepts

if b^2=4ac, there is one x intercept
b^2>4ac,there are two x intercepts
b^2<4ac,there are no x intercepts
and x is a complex number

in your equation b^2<4ac so the roots
are complex numbers

i hope that this helps

Answer 5

I think you are confusing the quadratic quation with linear equations. y = mx +b. The quadratic equation is used when x has two distinct values. When you have an expression in the form ax^2 + bx + c = 0 then you use the quadratic equation x = -b + or - sqr(b^2 - 4ac)/2a

to work the problem you simply plug in the variables and do it twice once for x = -b + sqr(b^2 - 4ac)/2a
and once for x = -b - sqr(b^2 -4ac)/2a

slopes, intercepts, etc. are different functions of linear equations. Hope this was helpful.

Answer 6

To simplify, c (896.2) is the y intercept.
The slope varies continuously, so there's no fixed value.
a & b (.0654 & 1.9506) are just the coefficients of the x^2 & x term.

a, b and c are used in the quadratic formula to determine x when y = 0 -------> x = (1/2a)(-b +-rt(b^2-4ac)) This may result in imaginary #s if the function graph doesn't cross the x axis.

Answer 7

When x=0 the y axis is intercepted at 896.2. The slope is a parabolic shape as it is a quadratic equation. The slope is therefore not constant for all x.

0.0654 is the quadratic coefficient. 1.9506 is the linear coefficient and 896.2 is the free term or constant.

You are welcome.

Answer 8

Quadratic Equation

ax² + bx + c

Click on the URL below for additiona Information concerning quadratic equation.

en.wikipedia.org/wiki/Quadratic_equation

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Slope formula

m = y₂- y ₁/ x₂- x₁

Slope Intercept form

y = mx + b

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Answer 9

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Answer 10

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut17_quad.htm