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Now here we have some problems related to the standard form of the quadratic equation.

1. Write the given equation: 2x = 4x^2 + 2 into standard form.

We have equation 2x = 4x^2 + 2

4x^2 – 2x + 2 = 0

2x^2 – x + 1 = 0 this is the standard form of the given equation.

Similarly we have one more problem.

2. Given equation is 4x – 4 = 7x, change it in its standard form.

The answer is that the given equation is not a quadratic equation so we cannot change it in its standard form.

A quadratic function is a polynomial function which has a standard form

f(x) = a(x – m)^2 +n

The graph of the quadratic function is U in shape and this shape is known as parabola in mathematics. To get the x-intercept and y-intercept of the graph we just change the values of all the three coefficients which are m, n, a.

In the above equation the term (x – m)^2 is either be positive or zero, because it is a square term i.e. (x – m)^2 > = 0.

In the case if we multiply a on both the (left and right) sides of the equation then the value of a will be either positive or negative. So here we have two possibilities:

1. Coefficient a is negative: a(x – m)^2

So add n on both the sides

a(x -m)^2 + n

Here a(x -m)^2 + n represents the function f(x) and f(x)

2. If coefficient a is positive: a(x – m)^2 >= 0

a(x -m)^2 + n >= n

Here f(x) >= n so n is the minimum value of the quadratic function f(x).

So in this session we learnt about the standard form, In order to get help on Graphing Linear Equations and Simplifying Expressions visit TutorVista.com.