Standard Fraction Standard form of Fraction: When numerator and denominator are co-prime, then the fraction is said to be in standard form. Two numbers are co-prime if they have no common factor other than 1. Following are some examples of fractions in standard form.

How to write numbers in standard form:

1. Write the first number 8.
2. Add a decimal point after it: 8.
3. Now count the number of digits after 8. There are 13 digits.
4. So, in standard form: 000 000 is 8.19 × 10¹³

Answer: It can be written as 1.47×10-³.

To convert from slope intercept form y = mx + b to standard form Ax + By + C = 0, let m = A/B, collect all terms on the left side of the equation and multiply by the denominator B to get rid of the fraction./span>

Going From Standard Form to Slope-Intercept Form

1. A standard form equation is when it is set up.
2. Ax + By = C.
3. 6x + 2y = 4.
4. A slope-intercept form equation is when it is set up y=mx+b.
5. Y = – 3x + 2.
6. 4y = -8x + 16 then divide all by 4.
7. y = -2x + 4 slope form.
8. Example 2:

Thus, to convert to point-slope form, first convert to slope-intercept form, then move the constant term b to the left side of the equation (or isolate x and then divide by the y coefficient). Example: Convert 3x = 4y + 8 to point-slope form.

First, find the intercepts by setting y and then x equal to zero. This is pretty straightforward since the line is already in standard form. Plot the x and y-intercepts, which in this case is (9, 0) and (0, 6) and draw the line on the graph paper!

An equation written in standard form is yet another equation that forms a parabola when graphed. Each letter in the standard form equation tells us a piece of information about the parabola, just like the letters from the vertex form equation had. “a”, can also tell us the width of a parabola.

Standard form, or standard index form, is a system of writing numbers which can be particularly useful for working with very large or very small numbers. Scientists use standard form when working with the speed of light and distances between galaxies, which can be enormous.

standard form is the usual way of writing numbers in decimal notation, i.e. standard form = 876, expanded form = 800 + 70 + 6, written form = eight hundred seventy six.

Standard Form. The quadratic function f(x) = a(x – h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

The form ax2 + bx + c = 0 is called standard form of a quadratic equation. Before solving a quadratic equation using the Quadratic Formula, it’s vital that you be sure the equation is in this form. If you don’t, you might use the wrong values for a, b, or c, and then the formula will give incorrect solutions.

Summary

1. Quadratic Equation in Standard Form: ax2 + bx + c = 0.
2. Quadratic Equations can be factored.
3. Quadratic Formula: x = −b ± √(b2 − 4ac) 2a.
4. When the Discriminant (b2−4ac) is: positive, there are 2 real solutions. zero, there is one real solution. negative, there are 2 complex solutions.

You can see how this relates to the standard equation by multiplying it out: y=a(x−h)(x−h)+ky=ax2−2ahx+ah2+k . This means that in the standard form, y=ax2+bx+c , the expression −b2a gives the x -coordinate of the vertex.

Notes

1. Standard form of a quadratic equation is y=ax2+bx+c, where ‘a’ is not 0.
2. Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the quadratic function.

The standard form of a quadratic function is f(x)=a(x−h)2+k. The vertex (h,k) is located at h=–b2a,k=f(h)=f(−b2a)./span>

How to convert from the standard form to the vertex form?

1. Write the parabola equation in the standard form: y = a*x² + b*x + c ;
2. Extract a from the first two terms: y = a * (x² + b/a * x) + c ;
3. Complete the square for the expressions with x .

One way to write a polynomial is in standard form. In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to right./span>

Explanation: To find the degree of the polynomial, add up the exponents of each term and select the highest sum. The degree is therefore 6.

Polynomials. For an expression to be a polynomial term, any variables in the expression must have whole-number powers (or else the “understood” power of 1, as in x1, which is normally written as x). A plain number can also be a polynomial term.

(i) polynomial , because the exponent of the variable of 8 or 8×0 is 0 which is a whole number . (iii) Not polynomial ,because the exponent of the variable of 1-√5xor1-√5×12)is 12 which is not whole number. (viii) Not polynomial , because the exponent of the variable of 12xor12x-1 is -1 which is not a whole number./span>