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Algebra

Algebra. 3.7 Formulas and Functions. Formulas. A formula is an algebraic equation that relates two or more real-life quantities Formulas have more than one variable Formulas are used in science, business, geometry and everyday life. rt = d p = 2l + 2w A = ½bh V = lwh

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Algebra

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  1. Algebra 3.7 Formulas and Functions

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

  3. 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.

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

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

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

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

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

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

  10. Rewrite the equation in Function Form (isolate y) 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 = - 10x + 35 y - 7 = 7x - 9x 5 y - 7 = -2x 5 +7 +7 (5) y = (-2x + 7) (5) 5 y = -10x + 35

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

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

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