Concept explainers
For Exercises 41–50, write the standard form of the equation of the hyperbola subject to the given conditions. (See Example 5)
Vertices:
Foci:
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College Algebra (Collegiate Math)
- Find a or k so that the points (-5,-8) and (1,-25) lie on the parabola y=a(x+3)²+karrow_forwardWhich are the foci for the hyperbola modeled by the equation (X-32 (x-1)²-1? 36 13 O (1. 10) and (1,-4) O (3.8) and (3, -8) O (1.9) and (1, -3) O (-6, 0) and (6, 0)arrow_forwardIn Exercises 85–88, find the vertex for each parabola. Then determine a reasonable viewing rectangle on your graphing utility and use it to graph the quadratic function. 85. y = -0.25x² + 40x 86. y = -4x? + 20x + 160 87. y = 5x² + 40x + 600 88. y = 0.01x² + 0.6x + 100arrow_forward
- 3) Explain how changing the a, h, and k variables affect the shape of the parabola in the vertex form y = a(x - h)² + k. [3 Communication Marks] Page 1arrow_forwardWhich parabola has a vertex at the (0, 3) and opens to the right? O y=x²+3 O y = -(x + 3)² Ox=y²-3 O x = (y - 3)² O-(x+3)² = (y - 3)²arrow_forward3) Put x2 + 6x - y = 8 in standard (vertex) form %3Darrow_forward
- 2. Suppose that the last three digits of your student number are like. abc . It is not important whether it is a 4 digit number or a 5 digit number, take the last three :+(-1) ; (b+1)3 digits as abc. Consider the conic (-1)ª following. Major semiaxis Minor semiaxis (-1)ab. Find the %3D (a+1)a i. ii. iii. Vertices iv. Foci Eccentricity Directrices Asymptotes (if it is a hyperbola) and the graph (geogebra or nice handmade) V. vi. vii. Now, consider the Quadratic Surface (-1)ª. (a+1)a +(-1) + (-1)° (b+1) =(-1)abe. (c+1)2 Find the following. Name of the surface viii. ix. Traces of the surface Nice Graph (in GeoGebra or handmade) х. For example, your professor's ID number is 0000005121. So, he will study the conic (-1) + (-1) =(-1)*2 which gives (-) + (-1)', (1+1) = (-1)12 which gives (-) + = 1. Also he will (2+1)3 4 study the quadratic surface (-1)' (1+1)2 + (-1)² - (2+1)a + (-1)'; :(-1)121 (1+1) which gives. (-) + + (-÷) = 1.arrow_forwardFind the equation of the parabola whose axis is parallel to the x-axis and passes through the points (3,1), (0,0), and (8,-4).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage