Consider f(x) = -(c+7)^2 + 4. Which of the following are true for f(x)? Check all that apply. Answer choices: the equation is a quadratic. The graph is linear. the vertex is (7,4). The axis of symmetry is x= -7. The y-intercept is (0,4). The graph has a relative maximum. The equation has no real solutions.

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answersare presentedbelow:TRUEFALSETRUEFALSETRUEFALSE## Quadratic function

The

quadratic functioncan be represented by a quadratic equation in theStandard form: ax²+bx+c=0where:a,bandcare your respectivecoefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and thedegreeof the functionmust be equal to 2.The

vertexof an up-down facing parabola of the form ax²+bx+c is . Knowing thex-coordinate of vertex, you can find they-coordinate of vertex. When a vertical line passes through the vertex of the parabola, it is called theaxis of symmetry.The

y-interceptis the point where the functioncrossesthey-axis.And, thex-interceptis the point where the functioncrossesthex-axis, in other words, wheny=0.First, you should

convertthe given equation toStandard form.f(x) = -(c+7)² + 4

f(x)= - (c²+14c+49)+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-45

After that, you should

checkeach option of the question.The equation is a quadraticCorrectbecause present a degree 2 -- f(x)= -c²-14c-45The graph is linearIncorrectbecause it is a quadratic function and this function is represented by aparabola.The vertex is (7,4)The coefficients are:

a=-1, b=-14, c=-45. Therefore,Incorrectbecausex-coordinate of vertexis-7The axis of symmetry is x= -7.CorrectbecauseThe y-intercept is (0,4)You can find

the y-intercept using c=0, then f(x)= -c²-14c-45 will be:f(x)=-45.

Incorrectbecause they-interceptis(0,-45).The graph has a relative maximum.Theand the values

coefficientof aaquadratic function is negative,thus the function has apoint maximum. Arelative maximum point is defined as thepointwhere the functionchanges your direction. In other words, the values of the functionincrease beforethe relative maximumdecrease afterthe relative maximum.Correct, see the attached image.The equation has no real solutions.It is possible to

find the number of rootsorsolutionsfromdiscriminant.For quadratic equation the

discriminantis determined byD=b²-4ac, where:a,bandcarecoefficients.If

D > 0- the function will havetwo real solutions;If

D = 0- the function will haveone real solution;If

D < 0- the function will haveimaginary solutions;For given equation, the coefficients are:

a=-1, b=-14, c=-45.Thus, D=(-14)²-4*(-1)*(-45)D=196-180=16

D=16thusD > 0Incorrectbecause theD>0.Read more about the

quadratic functionhere:brainacademy.pro/question/1497716