Mathematics, 08.12.2019 20:31 kyleee1991

An expression is shown below:

f(x) = 4x2 − 7x − 15

part a: what are the x-intercepts of the graph of f(x)? show your work. (2 points)

part b: is the vertex of the graph of f(x) going to be a maximum or minimum? what are the coordinates of the vertex? justify your answers and show your work. (3 points)

part c: what are the steps you would use to graph f(x)? justify that you can use the answers obtained in part a and part b to draw the graph. (5 points)

Answers: 3

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Answers

Part A: The x-intercepts aro those values of x that makes f(x) equal to zero. To find those values (that are called the roots of the equation), we just need to apply a well known formula: , where "a" is the coefficient that accompanies the quadratic term (in this case a=4), "b" is the coefficient that accompanies the linear term (in this case b=-7) and "c" is the constant (in this case c=-15). Then, replacing the values into the expression will give us the values of x that makes f(x) equal to zero, which are the x-intercepts:

.Then, the x-intercepts will be , and

Part B: The vertex of f(x) is going to be a minimum. This is because the sign of the quadratic term is possitive, then the quadratic equation has a form of "U",which means that it will reach a minimum value (in the vertex of the U coordenates) and then it will grow up infinitely. When the sign of the quadratic term is negative, the quadratic function is upside down, and it has the form of a bell, which means it will reach a maximum value in the top of the bell, and then it will decrease infinitely.

There is a formula to find the vertex. The vertex will be expressed as a coordenate that will indicate where the minimum value is placed in terms of x and y axis. The formula says that the x coordenate of the vertex is obtain from the following expression: , where "a" and "b" are the coefficients that accompany the quadratic term and the linear term respectively, as explaned in part A. To find the y coordenate, we just have to replace into the equation f(x), like this: , then .We now have the pair of coordenated from our vertex!

Part C: To graph the quadratic function, we have all information we need. We know that the function has two x-intercepts that take the values of and , and that the minimum value of the function is placed in . If we allocate the vertex, and mark the x-intercepts, we just have to connect the vertex to the intercepts to get the graph of our function!

Answer from: Quest

step-by-step explanation:

Answer from: Quest

answer is 144

step-by-step explanation:

$(x^{\frac{1}{8} }) (x^{\frac{3}{8} }) = 12\\$