Identifying Quadratic Equations

Student can identify the standard form of a quadratic equation and mathematically represent real-life situations.

8 lessons

Preview · progress not saved — Chapter 1 is free

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concept

What is a Quadratic Equation?

Definition of standard form.

A quadratic equation in the variable $x$ is an equation of the form $ax^2 + bx + c = 0$ , where $a$ , $b$ , and $c$ are real numbers, and crucially, $a \neq 0$ .

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Standard Form

Formula card for ax^2 + bx + c = 0.

a x^{2} + b x + c = 0

Variable

x

Constants

a, b, c (re a l n u mb ers)

a ≠ 0
Otherwise it becomes a linear equation.

Example:

2 x^{2} + x - 300 = 0

a = 2 · b = 1 · c = −300

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worked example

Example 1: Translating Word Problems

Representing a real-world situation mathematically.

The Problem

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with. Let's represent this mathematically.

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worked example

Example 2: Checking Equations

Simplifying an equation to check if it is quadratic.

The Problem

Check whether the following is a quadratic equation: $(x - 2)^2 + 1 = 2x - 3$

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Checking Hidden Quadratics

Faded example on checking cubic-looking equations.

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Let's check if the equation $(x + 2)^3 = x^3 - 4$ is quadratic. At first glance, it appears to be a cubic equation because of the degree 3 terms.

First, expand the LHS using the formula for a cubed binomial: $x^3 + 6x^2 + 12x + 8$ . Now, equate this to the RHS: $x^3 + 6x^2 + 12x + 8 = x^3 - 4$ .

Notice that if we subtract $x^3$ from both sides, the cubic terms .

By bringing all terms to one side, we get $6x^2 + 12x + 12 = 0$ . Because its highest remaining power is 2, this equation a quadratic equation.

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quiz

Identify the Quadratic Equation

Select which equation is quadratic.

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Which of the following equations simplifies into a true quadratic equation?

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← backNCERT X - Mathematics next →Solving By Factorisation

concept

What is a Quadratic Equation?

Definition of standard form.

A quadratic equation in the variable $x$ is an equation of the form $ax^2 + bx + c = 0$ , where $a$ , $b$ , and $c$ are real numbers, and crucially, $a \neq 0$ .

1 / 3

worked example

Example 2: Checking Equations

Simplifying an equation to check if it is quadratic.

The Problem

Check whether the following is a quadratic equation: $(x - 2)^2 + 1 = 2x - 3$

1 / 4

reading

Checking Hidden Quadratics

Faded example on checking cubic-looking equations.

0 of 2 blanks filled

Let's check if the equation $(x + 2)^3 = x^3 - 4$ is quadratic. At first glance, it appears to be a cubic equation because of the degree 3 terms.

First, expand the LHS using the formula for a cubed binomial: $x^3 + 6x^2 + 12x + 8$ . Now, equate this to the RHS: $x^3 + 6x^2 + 12x + 8 = x^3 - 4$ .

Notice that if we subtract $x^3$ from both sides, the cubic terms .

By bringing all terms to one side, we get $6x^2 + 12x + 12 = 0$ . Because its highest remaining power is 2, this equation a quadratic equation.

quiz

Identify the Quadratic Equation

Select which equation is quadratic.

1 / 5

Which of the following equations simplifies into a true quadratic equation?