Mathematics, 17.07.2019 00:00 sliim89

Find the x-intercept of the parabola with vertex (-3,-14) and y-intercept (0,13)

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If there is one x-intercept, then there is 2. First we have to use the information given to write the equation for the parabola. Then we can factor it, because factoring is what finds the zeros (aka x-intercepts, roots, and solutions) of the function. We know from the fact that the y-intercept is above the vertex that this is an upwards-opening parabola. The standard form of a parabola of this nature is $y=a(x-h) ^{2}+k$ . We have the h and k from the given vertex, and we have the x and y from the y-intercept. We will use all that to solve for a. $13=a(0+3) ^{2} -14$ . When we simplify that down we get 13 = 9a - 14 and 9a = 27. Therefore, a = 3. Now we can write the equation for the parabola. $y=3(x+3) ^{2}-14$ . But we can't solve for x the way it is without simplifying that completely. We need to expand that binomial, and when we do that we have $y=3( x^{2} +6x+9)-14$ . Then we have to distribute in the 3 and then subtract 14 at the end. That will give us, finally, $y=3 x^{2} +18x+13$ . Now we can set that equal to 0 and factor it. The x-intercepts exist when y = 0; when y = 0, we have x-values only, which are the places where the graph goes through the x-axis. Putting those values into the quadratic formula, we find the 2 zeros of the function are x = -.839 and -5.16

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step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring). so find the distance between (1,2) and (4,2). that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3. it is a regular polygon which means all sides are congruent. you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

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steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.

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Find the x-intercept of the parabola with vertex (-3,-14) and y-intercept (0,13)...