Quadratic Equation
Understand and solve quadratic equations in Grade 9 algebra. Write equations in standard form ax²+bx+c=0 and solve by factoring, completing the square, or the quadratic formula.
Key Concepts
Property A quadratic equation is an equation whose graph is a parabola. The standard form is $ax^2 + bx + c = 0$. Explanation Think of it as any equation where the variable's highest power is two, creating a U shaped parabola graph. Before using the quadratic formula, you must arrange the equation into its standard form, $ax^2 + bx + c = 0$. This ensures you correctly identify the $a$, $b$, and $c$ coefficients for the formula. Examples The equation $ 18x + x^2 = 32$ is rearranged into standard form as $x^2 18x + 32 = 0$. The equation $16h^2 + 25 = 40h$ is rearranged into standard form as $16h^2 40h + 25 = 0$. The equation $x^2 + 80 = 21x$ is rearranged into standard form as $x^2 21x + 80 = 0$.
Common Questions
What is a quadratic equation?
A quadratic equation is a polynomial equation of degree 2 written as ax² + bx + c = 0 where a ≠ 0. The squared variable is always the highest power term.
What are the three main methods for solving quadratic equations?
Factor and use the zero product property, complete the square to transform to vertex form, or apply the quadratic formula x = (-b ± √(b²-4ac)) / 2a for any quadratic.
How do you put a quadratic equation into standard form?
Move all terms to one side so the other equals 0. Write in descending order: ax² first, then bx, then constant c. Example: 2x² - 5 = 3x becomes 2x² - 3x - 5 = 0.