Equations of linear functions are graphed as straight lines because the x variable does not have an exponent. Quadratic functions are graphed as curves because the variable does have an exponent. Linear and quadratic equations can be solved either algebraically or graphically. In these worksheets, student will learn how to solve linear and quadratic functions algebraically. They will then gain proficiency by practicing the skill. They will equate linear and quadratic equations and find
the value of y; they will then solve for the solution set. A prior understanding of algebra is required. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. When finished with this set of worksheets, students will be able to recognize basic properties of a parabola by studying its equation.
These worksheets explain how to solve linear and quadratic equations algebraically. Sample problems are solved and practice problems are provided.
This worksheet explains how to solve the equation for y : y= 4x - 6. Substitute the value of y in quadratic equation: 4x - 6= x2 -4x + 14; 14 + 6 = x2 - 4x - 4x. A sample problem is solved, and two practice problems are provided.
Students will tackle linear and quadratic functions with the focus on putting together an algebraic solution. Three problems are provided, and space is included for students to copy the correct answer when given.
How to Solve Quadratic Functions Algebraically?
Factoring is also known as "middle-term break."
Start by finding the product of 1st and last term.
Find the factors of product 'ac' in such a way that the addition/subtraction of these factors equals the middle term.
Now write the center term using the sum of the two new factors.
Form the following pairs; first two terms and the last two terms.
Factor each pair by finding common factors.
Now, factorize the shared binomial parenthesis.
The second method is completing the square method;
Start by transforming the equation in a way that the constant term is alone on the right side.
If the leading coefficient is not equal to 1, divide both sides by a.
Now, add the square of half the coefficient of the x -term, to both sides of the equation.
The next step is to factor the left side as the square of a binomial.
Proceed by taking the square root of both sides and then solve for x.
The third method is through the use of the quadratic formula;
It simply requires one to substitute the values into the following formula;
x=(-b ± √(b2 - 4ac)) / 2a
The fourth method is through the use of graphs.
The roots of a quadratic equation are the x-intercepts of the graph.
