Rewriting a Quadratic Equation in Standard Form
Grade 9 students in California Reveal Math Algebra 1 learn how to rewrite any quadratic equation into standard form ax²+bx+c=0 where a≠0. This skill requires collecting all terms on one side using addition or subtraction so the other side equals zero. For example, x²+3x=10 becomes x²+3x-10=0 (a=1, b=3, c=-10), and 2x²=5x-3 becomes 2x²-5x+3=0 (a=2, b=-5, c=3). Once in standard form, students can define the related quadratic function f(x)=ax²+bx+c and graph it to find the solutions of the original equation.
Key Concepts
A quadratic equation is in standard form when it is written as:.
$$ax^2 + bx + c = 0, \quad a \neq 0$$.
Common Questions
What is the standard form of a quadratic equation?
Standard form is ax²+bx+c=0 where a≠0. All terms are on one side of the equation with zero on the other side, and the equation is arranged from highest to lowest degree.
How do you rewrite a quadratic equation in standard form?
Use inverse operations to move all terms to one side of the equation so that the other side equals zero. Then combine like terms and arrange from highest to lowest degree.
Why is standard form necessary before solving quadratics by graphing?
Standard form lets you define the related function f(x)=ax²+bx+c whose x-intercepts are the solutions. You must correctly identify a, b, and c before graphing the parabola to find intersection points.
How do you rewrite 2x²=5x-3 in standard form?
Subtract 5x from both sides and add 3 to both sides: 2x²-5x+3=0. Here a=2, b=-5, and c=3.
What is the related quadratic function once you have standard form?
After rewriting in standard form ax²+bx+c=0, the related function is f(x)=ax²+bx+c, which can be graphed to find the x-intercepts that solve the original equation.
Which unit and grade level covers this skill?
This skill is from Unit 10: Quadratic Functions in California Reveal Math Algebra 1, Grade 9.