Quadratic functions are used in algebra that are polynomial functions, that contaions one or more variables. In a quadratic function, the higest degree term is of second degree. It is also known as quadratic polynomial or polynomial of degree 2 and also simply quadratic. An example of quadratic function can be: f (x,y,z) = ax2 + by2 +cz2 + dxy + exz + fyz + gx + hy + iz + j
This quadratic function contains, variables like x, y and z and also contaions some exclusive terms like x2, y2, z2, xy, xz, yz, x, y, z, and a constant which is j. The second degree terms for the coefficients a, b, c, d, e, or f are non zero.
An example of a single variable or univariate quadratic function will be: f (x,y) = ax2 + bx + c , a "≠" 0
Here, c is a constant.
The graph that is being generated using a quadratic function is known as parabola. The parabolas have a basic “U” shape. Every parabola is symmetric with respect to the axis of symmetry. The points at which the parabola intersects the axis of symmetry is known as the vertex of the parabola.
Example 1: Solve then quadratic equation x2 – 8x + 14 = 0
The first step is to identify a, b and c from the given equation. In this case a = 1, b = –8, and c = 14.
The next step is to substitute the values in the quadratic formula,
Now, solve the equation,
Simplify the quation, if only there are chances of simplification,
The steps to do this correctly are:
Example 1: Solve the quadratic equation x2 + 16 = 10x
Step 1: x2 – 10x + 16 = 0
Step 2: Use factoring strategy
(x – 2)(x - 8) = 0
Step 3: Use the zero product property
x – 2 = 0 or x – 8 = 0
Step 4: Solve for each factor
x = 2 or x = 8
Example 2: Solve the quadratic equation 50x2 = 72
Step 1: Rearrange the equation 50x2 – 72 = 0
Step 2: Use the factoring strategy
2(25x2 - 36) = 0
2(5x + 6)(5x - 6) = 0
Step 3: Use zero product property
5x + 6 = 0 or 5x – 6 = 0
Step 4: Solve for each factor
5x = -6 or x = -1
x = - 6/5 or x = 6/5
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