1. Rewrite the relation y = -2x2 + 24x – 75 in vertex form by completing the square. What is the maximum or minimum value? Then use transformations to graph this relation. On your graph, label the vertex and the axis of symmetry.

Q: Determine the vertex- f( x)= x^2 +4x +3 O (2-1) (-2, -1) O (3,-1) O (1,-2)

A: given equation of parabola f(x)=x2+4x+3 we know vertex is the maximum of minimum of a parabola,…

Q: Determine whether the graphs of 6x - 3y = 10 and2x + y = - 8 are parallel, perpendicular, or…

A: Given equations are: 6x-3y=10 and 2x+y=-8 To determine whether the graphs of the given equations are…

Q: 3, write an ordered pair that must be on the graph of y = f(x ·

A: Given: f(-4) = -3       To determine: An ordered pair that must be on the graph of y = f(x-3) - 1.

Q: Describe how to obtain the graph of g and h if g6) = 2(x +2)- 3 m (x) = 2x? and h (x) = 2(x-3)2+2…

A: gx=2x+22-3, mx=2x2 and hx=2x-32+2   The graph of gx=2x+22-3 is obtained by horizontally shifting the…

Q: • Determine and draw the graph of the following equation in R3 : x2 + 212 + 2 8x + 12y – 2z + 35 = 0…

A: This is a problem of multi variable calculus, 3D geometry.

Q: What happens to the shape of the graph of x2/a2 + y2/b2 = 1 as c/a ⇒ 0, where c2 = a2 - b2?

A:

Q: 2. Describe how the graph of y = 2ƒ (²x) — 3can be produced from the graph of y = f(x). List all

A:

Q: Determine the concavity of the graphs of y^2=x and y=x^3

A: We have to determine the convexity of the graphs of y2 = x and y = x3 in between the points of their…

Q: Identify and sketch the graph of y = x² + 1 in R³.

A: Any point on the three dimensional coordinate system R3 can be represented by the point: x, y, z. A…

Q: Which point(s) lie on the graph of 3x 2y: 12? a) (6, 2) b) (-2, 3)

A: Solution a) If point lies on the graph, the point will satisfy the equation of the graph. Consider…

Q: fx) = 1 + 5x f(x) 2の 31 -2 -1 0. 2 17

A:

Q: y=X +, y= x+3 about the X-axis

A: L

Q: Determine whether the graphs of the two are parallel.  y+5=4x 3x-y=-5

A:

Q: Explain the difference between the graph of a n= n 2 and f(x) = x 2

A: Observe the following for the first function.

Q: Draw the graph of y + 2 = 7(x – 1).

A: Given- y+2=-23x-1 To draw- The graph of the above equation.

Q: Identify and sketch the graph of y = r²+1 in R³.

A:

Q: L6. y- x, Y=0, X=4, abut x-7

A: Given: y=x , x=4 , y=0 about x=7

Q: If (a, 2) is a point on the graph of y = 5x + 6 , then what is the value of a? a =

A: Given y=5x+6 (a,2) is point on this equation To find a

Q: Use the graph of 5 x Y = x² + 4

A:

Q: A student graphed f(x) = x and g(x) = -5f(x) + 2 on the same coordinate grid. Which statement…

A:

Q: Q26) Use shifting graph to sketch a) y = -|2x2 – 1 |+3

A: Our objective is to use shifting graph to sketch y= -|2x^2-1|+3

Q: If (-2,b) is a point on the graph of 2x+3y=2 ,what is b?

A: x,y=-2, b2x+3y=2

Q: Choose the true statement. a) For a quadratic relation, the second differences are increasing. O b)…

A: We want to find true statement from given statements.

Q: 5. Identify and sketch the graph of y = x² + 1 in R³.

A: To identify and Sketch: the curve y=x2+1 in ℝ3.

Q: If f(4) = – 1, write an ordered pair that must be on the graph of y = f(x+ 5) – 4

A: The solution is given below:

Q: Find all points of intersection of the graphs of x2 − y = 3 and x − y = 1.

A: Definition used -         Solution of equations using graph -       We graph both equations on the…

Q: Sketch the set of points such that r2 12. Choose the correct graph below.

A: follow next step

Q: The graphs of y = a-xand y = a (1/a)x are identical. Why

A: Simplify y=a1ax, using the quotient property of exponent, aman=am-n. To plot the graph of y=a1-x,…

Q: If ( a, -5) is a point on the graph of y = x2 + 6x , what is a?

A: Given, ( a, -5) is a point on the graph of y = x2 + 6x

Q: Describe one similarity and one difference between the graphs of x2/25 + y2/16 = 1 and (x - 1)2/25 +…

A: Consider the following equations of two ellipses, x225+y216=1 and x-1225+y-1216=1

Q: If ( a, 4) is a point on the graph of y = x2 + 3x , what is a?

A: Given, point (a,4) lies on the graph of equation y=x2+3x. To find: value of a. Solution: As (a,4)…

Q: Which ordered pair does not represent a point on the graph of y = 3x^2 - x + 7?

A:

Q: Which statement describes the graph off (x) = x² – 2x – 3? O A. a line with an x-intercept of(-1,0)…

A: Dear student, We are allowed to answer one question at a time and in case of multiple question we…

Q: The relation 2(x-4)° +6(:-5)* =12. represents the graph

A: 3D- graph plotting

Q: Describe and sketch the graph of the following: 3. x^2 − 9z^2 = 36

A: To sketch the graph of an equation, first for random values of one variable(the independent…

Q: State the equation of a relation whose vertex would be lower than the origin and to the left of the…

A: We have to find the equation of the relation whose vertex is lower than the origin and left to the y…

Q: What is the graph of xy = 0? Defend your answer.

A: Given, xy=0 ⇒y=0⇒x=0

Q: Are the graphs of x2 - y2 = 0 and y2 - x2 = 0 identical? Explain your answers.

A: Graphs for equations are plotted by putting random values of x in the equation to get random values…

Q: Determine the values of a and b in the relation y=ax^2+bx-42 if the vertex is located at (-4,6).

A:

Q: The manager of a local restaurant is trying to decide how much money to spend on advertising. She…

A: Sol:- First plot the given parabola R = -0.0005(A-5000)2+12500 Here R = Extra Revenue & A =…

Q: Which graph represents -2x +3y = -24?

A:

Q: Describe the transformations that you would apply to y=x² to get the graph of y =-3(x+4) -6. Then…

A: The vertical shift in the graph of y=f(x) is represented by the transformation function, y=f(x)±n…

Q: IDo y = X +5 X, X- axis

A: (10) The equation of the curves are : C1 : y = x2+5x C2 : x-axis To evaluate : The area bounded by…

Q: How do the graphs of y=1/x and y=5/x+6

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Q: Identify the following using the graph of y = 2V1-x- 6 2 10 -9 -8 -6 -5 -3 -2. X-Intercept: 2

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Q: d) What is the maximum height of the boarder?

A: Given, The gap is 2.2 m wide. And path modelled as h = -1.25d2 + 3.75d

Q: Determine the maximum or minimum value for each quadratic relation below. a) y = 2 (x - 5)^2 - 8…

A: (a) y = 2(x-5)² - 8 So, y' = 4(x-5) &, y" = 4  Now, for maximum or minimum values of y, we must…

Q: Find all points of intersection of the graphs of x2 − y = 3 and x − y = 1

A: To find the points of intersection, we solve both equations.

Q: Explain how to graph x2 + y2 = 1.

A: Given:Explain how to graph x2 + y2 = 1.