Tutor profile: Pavitra A.
Find the horizontal and vertical intercepts of the function f(x) = 3(x-1)^2-34
The horizontal intercepts occur when the function crosses the x-axis, which means that at those points, x=0. So we start by setting x to 0 in the equation which gives us f(0) = 3(0-1)^2-34 This simplified gives us f(0) = 3 - 34 = -31 This means that when x = 0, f(0) (which is the same thing as the y-value) is equal to -31. Therefore, the horizontal intercept is at (0, -31). The vertical intercepts occur when the function crosses the y-axis, which means that at those points, y=0. So we start by setting y to 0 (y is the same thing as f(x) so set f(x) to 0) which gives us 0 = 3(x-1)^2 - 34 Now we must solve for x. We do this by adding 34 from both sides, then dividing each side by three. Then we must take the square root of both sides (remember that when we take a square root, the answer is +/-). Finally, to isolate x, we must add one to both sides. This gives us the final answer, which is x = +/- sqrt(34/3) +1 This means that when y is 0, the x value can be sqrt(34/3)+1 or -sqrt(34/3)+1. Therefore, the vertical intercepts are at (sqrt(34/3)+1, 0) and (-sqrt(34/3)+1, 0).
Subject: Basic Math
Sally had 12 cupcakes. She and her three friends were at a picnic and she wants to share her cupcakes so that everyone gets an equal amount. How many cupcakes does each person get?
When we consider Sally and her three friends, there are four people total at the picnic. This means that 12 cupcakes must be shared equally between 4 people. In order to find the number of cupcakes each person gets, we have to use division. We can set up the equation like this: y = 12/4 When we simplify this equation, we are left with y = 3. This means that each person at the picnic gets 3 cupcakes each.
In the equation y = ((2+3)^2)*3/2, can you tell me the order in which you would simplify to find the answer? (Hint: use PEMDAS)
PEMDAS is an acronym for the order of operations and goes like this: Parentheses Exponents Multiplication/Division (whichever is first when reading from left to right) Addition/Subtraction (whichever is first when reading from left to right) Using this acronym, we would first find the innermost set of parentheses which is the (2+3). Simplified, this would be 5 and the equation would become y = (5^2)*3/2 Then we would go onto the next set of parentheses, which is (5^2) and simplify. This would give us y = 25*3/2 Next using the M and D part of PEMDAS, we would start simplifying from left to right. So first we would do the 25*3 which gives us y = 75/2 And finally, we would do the 75/2 which would give us the final answer y = 37.5
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