Study Tip: Write a note card explaining the mnemonic FOIL.
#Quadratic equation graph how to
Multiplied x by 5x and 3 and multiplied 2 by 5x and 3.įOIL is a simple mnemonic to remember how to multiply two binomials. Rule: To multiply two binomials, multiply each term of the first by each term of the second. Vocabulary: A binomial has two terms (just as a bicycle has two wheels). Multiplied the revenue equation by 1 and the cost equation by -1. Substituted the revenue and cost equations into the formula for profit. Used the distributive property and multiplied the revenue equation by 1 and cost equation by -1. If the revenue equation for a company is:įind the profit equation for the company.
The equation for profit is: Profit = Revenue - Cost Used the distributive property and combined like terms.Įxample 5. After that, we multiplied 6x by 3 and then -5 by 3. Recall the distributive property: Definition a(b + c) = ab + ac.Ĭouldn't combine the unlike terms inside the parantheses so we used the distributive property. Rule: To combine like terms, add their coefficients For example, the coefficient of 2x is 2, and the coefficient of -x 2 is -1. For example 2x 2 and 5x 2 are like terms while 3x 2 and 7x are not.Ī coefficient, originally presented in Section 1.3, "Simplifying Algebraic Expressions," is the number multiplying the variable. Like terms, originally presented in the Section 1.3, "Simplifying Algebraic Expressions," have the same variable and the same exponent. Vocabulary: To add or subtract quadratics, combine like terms. You will learn how to find them in the next Section 4.2, "Applications of the Quadratic Formula." You will learn how to find the vertex in Section 4.3, Quadratic Applications and Graphs.Īccording to the graph, the rock is on the ground at zero seconds (right before the boy shoots it) and at 4 seconds (when the rock lands). The maximum or minimum point of a quadratic is called the vertex. The points have the form (t, h).Īccording to the graph, the rock reaches its greatest height at 2 seconds. The height of the rock depends on the time, so h is the dependent variable, and t is the independent variable. Graph the points obtained in parts a through e. The rock is zero feet in the air at 4 seconds that is, the rock has hit the ground.į. In the formula, h = -16t 2 +64t, replace t with 4. The rock is 48 feet in the air at 3 seconds.Į.ğind the height of the rock when t = 4. In the formula, h = -16t 2 + 64t, replace t with 3. The rock is 64 feet in the air at 2 seconds.Įxplanation: Order of operations requires that you apply exponents before multiplying.ĭ.ğind the height of the rock when t = 3. In the formula, h = -16t 2 + 64t, replace t with 2. the -16 is multiplied by 1 2Ĭ.ğind the height of the rock when t = 2. The rock is 48 feet in the air at one second.Įxplanation: Only the "1" is being squared. In the formula, h = -16t 2 + 64t, replace t with 1. (This is the point right before he shoots the rock in the air.)ī.ğind the height of the rock when t = 1. The rock is zero feet in the air at zero seconds.
In the formula, h = -16t 2 + 64t, replace t with 0. The quadratic equation that models the height of the rock isĪ.ğind the height of the rock when t = 0. A boy lying on his back uses a sling shot to fire a rock straight up in the air with an initial velocity (the force the boy uses to fire the rock) of 64 feet per second. This feature of quadratics makes them good models for describing the path of an object in the air or describing the profit of a company (examples of which you may see in Finite Mathematics or in Microeconomics.)Įxample 1. Why study quadratics? The graphs of quadratic equations result in parabolas (U shaped graphs that open up or down). The slope-intercept equation from the second chapter, y = mx + b is called a first degree polynomial because the highest exponent is one. Quadratics are also called second degree polynomials because the highest exponent is 2. Vocabulary: The standard format of a quadratic equation is y = ax 2 + bx + c a, b, c are constants x is the independent variable, and y is the dependent variable. In this section, you will add, subtract, multiply, and graph quadratics. Chapter 4 - QUADRATICS INTRODUCTION TO QUADRATICS Objectives
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