Algebra 3 7 Formulas and Functions Formulas q

Algebra 3. 7 Formulas and Functions

Formulas q A formula is an algebraic equation that relates two or more real-life quantities q Formulas have more than one variable q Formulas are used in science, business, geometry and everyday life. rt = d Distance Formula p = 2 l + 2 w Perimeter of a rectangle A = ½bh Area of a triangle V = lwh Volume of a rectangular prism C = 5/9 (F-32) Temperature conversion (F to C)

Solving a formula When we solve a formula for an indicated variable, you simply isolate that variable on one side of the equation. To do this, you use inverse operations.

Solve the triangle area formula: Solve for b A = ½bh Ask yourself, where is the b and what’s happening to it. (2) A = ½bh (2) The b is being multiplied by ½ and by h, so you want to divide by½ (multiply by 2)…. . 2 A = bh h h 2 A = b h and divide by h. So, b = 2 A h

Solve the rectangle perimeter formula: Solve for w P = 2 l + 2 w Ask yourself, where is the w and what’s happening to it. P -2 l The w is being multiplied by 2 and that product is being added to 2 l, so first subtract 2 l…. . = 2 l + 2 w -2 l P – 2 l = 2 w 2 2 P – 2 l = w 2 and then divide by 2. So, w = P – 2 l 2

Try these yourself! n n Solve for h: Answer: V = l wh h= V lw Solve for F: C = 5 (F – 32) 9 Hint: First isolate (F – 32) Answer: F = 9 C + 32 5

Functions q A function is a rule that establishes a relationship between two quantities, called the input and the output q A linear function usually uses the variable x to describe input, and y to describe output q A two-variable equation is written in function form if the y is isolated on one side of the equation Function form: The output y y = 2 x + 4 is a function of the input x

Writing Function Form (you will learn why you do this later) q When you write the equation in function form, arrange the terms in the order below: Function form: Put the y on the left y = mx + b Put the x term first on the right Put the constant last Write the fractions out as individual terms, such as 4 x and 1 x 5 3

Rewrite the equation in Function Form (isolate y) 2 x + 3 y = 10 Ask yourself, where is the y and what’s happening to it. 2 x + 3 y = 10 -2 x The y is being multiplied by 3 and that product is being added to 2 x, so first subtract 2 x…. . 3 y = -2 x + 10 3 3 y = - 2 x + 10 3 3 and divide by 3. So, y = - 2 x + 10 3 3

Rewrite the equation in Function Form (isolate y) y - 7 = 7 x - 9 x 5 y - 7 = -2 x 5 +7 +7 (5) y = (-2 x + 7) (5) 5 y = -10 x + 35 First, simplify the right side. Next, add 7 to get the y term alone Then, multiply by 5. Make sure that you multiply EVERY TERM on BOTH SIDES by 5 So, y = - 10 x + 35

Now you try these n n Rewrite in function form: x + 2 y = 6 Answer: y = -1/2 x + 3 Rewrite in function form: 1 y + 3 = -5 x 4 Answer: y = -20 x - 12

Homework pg. 177 # 11 -29, 34 -39 (calculator OK on these)