Write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point.

Vertex: $(4,1)$; point: $(2,-1)$

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ=12 cm. Length PQ is :
(A) $12 \mathrm{~cm}$ (B) $13 \mathrm{~cm}$ (C) $8.5 \mathrm{~cm}$ (D) $\sqrt{119} \mathrm{~cm}$.

Is it possible for a Hamiltonian graph to contain a bridge? Explain.

Find the slope of the line that passes through the following pair of points.

$(3,-5)$ and $(-4,2)$

Given the formula: $P=a+b+c$, and the values:$P=48.5 \mathrm{~cm}, a=18.2 \mathrm{~cm}, b=24.3 \mathrm{~cm}$. Find $c$.

Find dy/dx of y= e raised to (x tan x)

Sketch a direction field for the differential equation y’=x/y. Then use it to sketch the four solutions that satisfy the initial conditions y(0) = 1, y(0) = -1, y(2) = 1, and y(-2) = 1.

Make a sketch to demonstrate each true statement. For each false statement, draw a sketch and explain why it is false. If a line and a plane have no points in common, then they are parallel.

Write the equation of the axis of symmetry, and find the coordinates of the vertex of the graph of each function. Identify the vertex as a maximum or minimum. Then graph the function.

$$y=x^2-4 x-4$$

Sketch the graph of the equation $y = \sqrt { x ^ { 2 } - 4 x + 4 }$ by translating. reflecting. compressing, and stretching the graph of $y = | x |$ appropriately. and then use a graphing utility to confirm that your sketch is correct.

For what values of r does the function y = e^rx satisfy the differential equation 2y’’ + y’ - y = 0?

Find the difference without using a number line.

$$-5-\dfrac{1}{2}$$

Find the equation of the line passing through the pair of points. (-2,-5),(4,-1)

Write the function in vertex form. Then identify the vertex and axis of symmetry of the function’s graph, and tell which direction the graph opens.

$$f(x) = x^2 – 2x + 5$$