Mathematics
Grade 10
15 min
Solve quadratic equations
Solve quadratic equations
What you'll learn
- Identify positive and negative integers on a number line with 80% accuracy.
- Explain the meaning of integers in real-world contexts (e.g., temperature, money, elevation) with at least three examples.
- Compare and order integers from least to greatest, using the symbols , or =, in at least 4 out of 5 comparisons.
- Solve simple addition and subtraction problems involving integers (e.g., -5 + 3, 2 - (-4)), achieving at least 70% accuracy on a worksheet.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify a quadratic equation and write it in standard form (ax^2 + bx + c = 0).
Solve quadratic equations by factoring when the leading coefficient is 1 and when it is greater than 1.
Solve quadratic equations by using the square root property and by completing the square.
Derive and apply the quadratic formula to solve any quadratic equation.
Use the discriminant to determine the number and type of solutions for a quadratic equation.
Choose the most efficient method to solve a given quadratic equation.
Model and solve real-world problems involving quadratic equations.
Ever wonder how a basketball shot arcs perfectly into the hoop or how engineers design the curve of a bridge? 🏀 The answer lies in quadratic equations!
This tutorial is a comprehensive...
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Key Concepts & Vocabulary
TermDefinitionExample
Quadratic EquationAn equation that can be written in the standard form ax^2 + bx + c = 0, where a, b, and c are real numbers and 'a' is not equal to zero. It is a second-degree polynomial equation.2x^2 - 5x + 3 = 0 is a quadratic equation where a=2, b=-5, and c=3.
Standard FormThe form of a quadratic equation where all terms are on one side, set equal to zero, and written in descending order of the variable's exponent.The equation 3x = 4 - x^2 written in standard form is x^2 + 3x - 4 = 0.
Roots (or Solutions)The values of the variable (e.g., x) that make the quadratic equation true. These are the points where the graph of the corresponding parabola intersects the x-axis.For the equation x^2 - 9 = 0, the roots are x = 3 and x = -3.
Zero Product Property...
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Core Formulas
Standard Form
ax^2 + bx + c = 0
Before solving, always rearrange the quadratic equation into this form. This helps identify the coefficients a, b, and c needed for other methods like the quadratic formula.
The Quadratic Formula
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
This formula can be used to solve any quadratic equation. It is especially useful when the equation cannot be easily factored.
The Discriminant
D = b^2 - 4ac
Calculate this value to quickly determine the nature of the solutions: If D > 0, there are two distinct real solutions. If D = 0, there is exactly one real solution (a repeated root). If D < 0, there are no real solutions (two complex conjugate solutions).
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Challenging
When deriving the quadratic formula by completing the square on the general form ax^2 + bx + c = 0, what is the key term added to both sides after dividing by 'a' and isolating the x-terms?
A.(\frac{b}{2a})^2
B.(\frac{b}{2})^2
C.b^2 - 4ac
D.c/a
Challenging
Which quadratic equation has the roots -5 and 3/2?
A.2x^2 - 7x - 15 = 0
B.2x^2 + 7x - 15 = 0
C.2x^2 - 13x + 15 = 0
D.2x^2 + 13x + 15 = 0
Challenging
The height h (in feet) of an object thrown upwards from a 112-foot tall building is given by h(t) = -16t^2 + 96t + 112, where t is the time in seconds. How long will it take for the object to hit the ground?
A.1 second
B.6 seconds
C.7 seconds
D.8 seconds
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Frequently asked questions
What grade level is "Solve quadratic equations"?
Solve quadratic equations is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Solve quadratic equations?
You'll be able to: Identify positive and negative integers on a number line with 80% accuracy; Explain the meaning of integers in real-world contexts (e.g., temperature, money, elevation) with at least three examples; Compare and order integers….
Is "Solve quadratic equations" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Solve quadratic equations?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.