Use optimization techniques to answer the question. Find the two real numbers x and y whose sum is 90 and whose product is as large as possible. (x, V) = (

Q: 14.What are the zeros of the function represented by the quadratic equation g (x) = 2x ?

A: Given that gx=2x2 find the zeros of the function

Q: How many zeros can a quadratic function have?

A: We have seen that a quadratic polynomial is of the form: fx=ax2+bx+c ,a≠0 We assume that a, b and c…

Q: Use the box method to distribute and simplify (-3x – 6)(-2x – 2). Drag and drop the terms to the…

A:

Q: Write the equation for a quadratic function f with integer coefficients that has the given zeros.…

A: a) ±bib) a±b i

Q: 3. Find expressions for the quadratic functions whose graphs are shown. (-2, 2), (0, 1) (4, 2)

A: Given that:

Q: Factor and find the zeros of the function y Justify your answer! 11. %3D 3x3 – 11x2 – 14x + 40

A: (x-a) is said to be a factor of a polynomial f(x) iff f(a)=0

Q: Use the method of completing the square to express f(x) = 3x - 24x + 58 in vertex form. %3D

A:

Q: Use a graphing utility to graph the quadratic function f(x) = −2x2 + 10x. Find the x-intercept(s) of…

A: x-intercept: The point at which the graph intersects the x-axis is called x-intercept.  Any…

Q: List the zeros of y = x(x +4). If you have more than one solution, separate them with commas.

A: Given that: y=x(x+4)

Q: Use calculus to find two numbers whose product is -16 and such that the sum of the squares of the…

A:

Q: Determine the quadratic function f. Simplify. The vertex is (3,-1) and the other given point is…

A:

Q: A dolphin dives down into the ocean and resurfaces along a path that is modeled by x² - 8x + 4y = 0,…

A:

Q: Select all the quadratic functions that you can easily factor to find their zeros. O A. f(x) = 2x² +…

A: To select the functions which can ve factored easily to find their zeroes.

Q: f (x) = 5ax – 2x².

A:

Q: All quadratic functions will factor, so finding the zeros by graphing is not needed. True O False

A: This is not always happen.

Q: What are the real root(s) of the quadratic equation whose related function is graphed below? A (3,0)…

A: The x-intercepts of the graph are the roots of concerned quadratic equation.

Q: Solve 2x2 -x-1=0 using the Quadratic Formula. Select all that apply. x=-2 x=-1 1 12 x= 2 no real…

A: To solve the given equation using the quadratic formula

Q: The graph of a quadratic function intercepts the x-axis in two places and the y-axis in one place.…

A: We know that ,  The fundamental theorem of algebra states that you will have n roots for an nth…

Q: Explain, . the process of completing the square on a quadratic function with leading coefficient 1,…

A: x2+bxMultiply and divide 'bx' term by 2x2+2bx2=x2+2b2x

Q: Solve cquation for X C. 2-xa %3D

A:

Q: Use the Intermediate Value Theorem to prove thateach equation has a solution. Then use a graphing…

A: Let us consider the interval [-2,2]  Let, f(x)=2x3 - 2x2 - 2x + 1 f(x) is a polynomial function, so…

Q: Find the solution of the following polynomial inequality. Express your answer in interval notation.…

A:

Q: Use this The quadratic function y = 2x + 3x-20 has zeroes at x = -4 and x 5 information to find the…

A: This question is based on mid-point Theorem. Mid-point of (a,b) and (c,d) is  x = (a+c)/2 , y =…

Q: True or False The equation x2 + 2x = (x + 1)2 - 1 is anidentity

A: Given : The statement, The equation x2 + 2x = ( x + 1)2 - 1 is an identity . The statement is true.…

Q: Find the X and Y intercepts of  y= 1 - the square root of 1 -x2

A: Given,

Q: Find all real solutions  square root of x-3=x-3

A:

Q: the zeros  of a cubic function are -1,-2/3,and 5. what are all the factors of (x).

A:

Q: The quadratic function y = 2x² + 3x - 20 has zeroes at x = -4 and x information to find the vertex…

A: We can find the vertex of the given quadratic equation as below.

Q: Use the quadratic formula to find the x- intercepts of y = x2 - 8x + 12 (Note: x is squared) Given y…

A:

Q: how many zeros are in the solution to the function g(x)=x2-3x+4

A: SOLUTION-

Q: A certain quadratic function has the factors (2x−5) and (3x+4). What are the zeros of the function?

A: To find the zeros of the function we have to set the factors equal to 0, and then solve for x. Given…

Q: What is the maximum number of real distinct roots that a quartic equation can have? a) infinitely…

A: ## we want to find out that how many real distinct roots that a quartic equation can have.

Q: An equation that is true for all real values in the domain of the variable is an ________.

A: We have to fill in the blanks: An equation that is true for all real values in the domain of the…

Q: Find all real solutions of the equation.

A: Any equation of form ax2+bx+c=0 is a quadratic equation as the highest exponent of a variable is 2 .…

Q: Rewrite the quadratic function f(x) = x2+ 10x – 9 in standard form, f(x) = a(x - h)2+ k, and give…

A: Given function is f(x)=x2+10x-9

Q: Calculate the real values of x and y such that (x+y)3 is bigger than 8?

A: Given, x+y3>8

Q: Solve for x by factoring. Must show all work  a) 3x2-12x=0 b) x2+4=-4x c) 3x2-x-10=0

A: (a) We have, ⇒3x2-12x=0⇒3x(x-4)=0         (taking 3x common)∴ 3x=0     and    x-4=0⇒x=0      and…

Q: the quadratic equation x2 + x = 3kx- k2 has two different real roots. find the range of value of k

A: The given problem is to find the range of value of k for which the quadratic equation has two…

Q: What is the axis of symmetry for f(x) = 2x² – 4x + 5? %3D Ox=-2 Ox = -1 Ox = 1 Ox= 2

A:

Q: Find the domain of f(x)=the square root of (16/x^2)

A:

Q: solve

A: Please refer to the image below

Q: Solve the giv '= .3 X x³ - 2y

A:

Q: Is there a real number ______ whose square is -1? b. Does there exist _____ such that x 2 = −1?

A:

Q: The area of a circle is equal to the product of π and the square of the diameter. true or false

A: Our Aim is to tell whether the statement stating that "The area of a circle isequal to the product…

Q: Find a quadratic polynomial whose zeroes are (i)3, -4 (i)2, 1

A: Quadratic  equation = x2-(Sum of zeroes)x + product of zeroes =0

Q: A rectangular box for a new product is designed in such a way that the Three dimensions always have…

A: Given: A rectangular box for a new product is designed in such a way that the Three dimensions…

Q: x" + 4x = 0 %3D

A: Given the differential equation is x" + 4x = 0. Here the auxiliary equation is m2 + 4 = 0

Q: Drag the appropriate answers from the choices given into the boxes provided. Identify the quadratic…

A:

Q: use quadratic functions. Find two numbers whose sum is 30, such that the sum of the square of one…

A: Given :                The two numbers whose sum 30 is…