Not so long ago, you learned in this course that the vertex of the parabola y = ax? + b bx + c occurs at x = 2a - You remember that, right? Use calculus to prove this fact. Hint: What should the slope of the tangent line be at the vertex? vertex X-axis -1- vertex -2 10 X-axis y-axis to SIxe-A

Q: 4x2 Trace the curve y? %3D (x+5)(x-2)

A: Given function is y2=4x2x+5x-2  ....1

Q: If f (x) = 2(x - 3)2- 8, Which of the following choices is an equation for the same parabola as f…

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Q: Q3// Does the parabola y = 2x2 - 13x + 5 have a tangent whose slope is (-1)? If so, find tangent and…

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Q: Find the slope of the curve y =x' – 2x at the point P(2,-2). .3 4

A: Given the equation of the curve,                                           y=14x3 - 2x and the point…

Q: A badminton birdie is hit along an arc described by the parabola h(x) -0. 1x² + x + 2.4, where h is…

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Q: 2. A projectile is fired from a cliff 200 meter above the water at an inclination of 45° to the…

A: Given situation in picture:

Q: Show your work and draw box(es) around your final answer(s). If you solve algebraically, show all of…

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Q: Quadratic functions a. Show that if la, fla22 is any point on the graph of f1x2 = x², then the slope…

A: (a) We have given the function;

Q: Find an equation for the circle with center (3, -4) and radius 2. 2+4 Find the domain of the…

A: Standard equation of circle with centre (h,k) and radius r is given by  (x-h)^2+(y-k)^2=r^2 Now, for…

Q: line has a slope of 2 and intersects the quadratic function f(x) = x(x-6) exactly once. Wha e…

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Q: Pls help ASAP

A: Given , the graph of f(θ) has the y-intercept at 3.

Q: Suppose you are climbing a hill whose shape is given by the equation z = 2,000 - 0.005x - 0.01y,…

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Q: Write down the equation of a straight line which passes through the origin and does not x 2…

A: Given curve is  y=x2-2x                     (i) Let the equation of the line passing through origin…

Q: Find an equation to model the vertical motion of the tip of a second hand on a clock, if the second…

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Q: I am on a planet whose acceleration due to gravity is g=6 ft/s2. I'm standing on a cliff edge with…

A: Consider the equation

Q: Find an equation of the line tangent to graph of F(x) x² + 1 x²_4 2 (3,2). write the equation in the…

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Q: 3. The shape of an underground pool follows a parabola with the function f(x) = x2 + 8x. What point…

A: we are given the equation of the parabola and we need to find out the lowest point of the parabola.

Q: Find the point at which the line f(x) = 3x + 15 intersects the line g(x)=x+7

A: given  f(x)=3x+15g(x)=x+7for intersection f(x)=g(x)

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.