Homework 12 Name: Show all work. You should avoid calculator usage unless you are using it to check your work. Also, you should be doing your work in pencil. Fundamental Questions 1) State the equation of the axis of symmetry to a parabola given by y = ar? + br + c. 2) What is the coordinate of the y-intercept to a parabola given by y = ar? + br + c? 3) Which constant out of a, b, or c determines whether the parabola given by y = ar? + br + c opens upward or downward? State the rule. 4) How can the r-intercept(s) be found given y = ax? + bx + c? 5) How is the vertex to the parabola given by y = ar? + br + c found? Routine Questions 6) Graph the parabola given by the following quadratic equation. Do not graph by plotting random points from a table of values. Instead, show your work to find the r- and y-intercepts, vertex, and axis of symmetry. y = 2x + 6.x +4'3) Graph the parabola given by the following quadratic equation. Do not graph by plotting random points from a table of values. Instead: Show your work to nd the I and y-intereepts, vertex: and axis of symmetry. y=-11'2+Eu:l 8) Graph the parabola given by the follawing quadratic equation. Do not graph b1. plotting random points from a table of values. Instead: Show your work to nd the z and yLintereepts. vertex, and ends of symmetry. y=3:23r+'?5 9) Graph the parabola given by the following quadratic equation. Do not graph by plotting random points from a table of values. Instead, show your work to find the r- and y-intercepts, vertex, and axis of symmetry. y= r + 2r + 10Old Exam Questions 10) A parabola y = r' + pr + q has an r-intercept at (-1, 0) and a y-intercept at (0, -8). Find the coordinates of the other r-intercept. You have to present an algebraic solution. Answers by drawing and guessing will give no credit.11} A parabola y = (1.:1 + In: + c has its 1mm: in the semnd quadrant and a negative yintercept. Determine the signs of :11 b1 and c. Justify your answer. Homework 13 Name: Show all work. You should avoid calculator usage unless you are using it to check your work. Also, you should be doing your work in pencil. Fundamental Questions 1) State the equation for the area of a circle with radius r. 2) State the equation for the circumference of a circle with radius r. 3) State the equation for the area of a triangle with base b and height h. 4) State the Pythagorean Theorem for a right triangle with legs a and b and hypotenuse c. Routine Questions 5) The hypotenuse of an isosceles triangle is 24 meters long. Find the lengths of the legs of the triangle. 6) One side of a rectangle is 2 inches longer than the other side. Find the lengths of both sides if the area of the rectangle is 15 square inches.7) According to Newton's law of universal gravitation, mim2 F = G" R2 where F is the force between the masses of m, and m2, G is the gravitational constant, and R is the distance between the centers of the masses. Use this equation to express R in terms of F, G, my, and mz- 8) An isosceles triangle is inscribed in a circle which is inscribed in a square with side length r. Write an equation (in terms of r) for the area of the shaded region below. If the area of the shaded region is 36 square inches, what must be the value of a? I9) A cardboard right circular cylinder 1with radius r and height h is cut to lay at on a table. Use the pictures below to create a formula for the surface area of the cylinder. If the height of the cylinder is 4 meters. and the surface area is 4211 square meters! what is the measure of the radius of the cylinder? Old Exam Questions 10) One leg of a right triangle is 11 inches longer than the other. The area of the triangle is 21 square inches. Find the lengths of the legs of the triangle. Solve the problem by composing an equation. Answers by guessing will give no credit. 11) The total energy of a system is given by the formula E = 2 + mgh . Use this formula to express v in terms of E, m, h, and g. Simplify your