What is the equation, in standard form, of a parabola that contains the following points? (–2, –22.5), (0, –?
y = 4.5x2 – 1.5x + 1.5
y = 1.5x2 – 4.5x – 1.5
y = -4.5x2 + 1.5x – 1.5
y = 1.5x2 + 1.5x +4.5
Im not looking just an answer. I actually want to understand it.
Another question if you can help me is:
Solve by using tables. Give each answer to at most two decimal places.
7x2 + 5x – 3 = 0
0.39, –1.1
1.1, –0.39
0.78, –2.21
0.75, –0.75
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Verified answer
Part of your question got cut off. What are the second and third points?
You can determine the equation of a parabola from three points. Plug each pair of coordinates into the general equation ax² + bx + c = y. That gives you a system of three equations, which you must solve for a, b, and c.
Since it's a multiple-choice question, there is another way to do it. Plug each pair of coordinates into each of the equations and make sure that the equations stay balanced. There will be only one equation that works with all the points you are given.
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"Solve by using tables"--without seeing the tables, I can't help you. In fact, I've never been asked to solve a quadratic equation by looking stuff up in tables.The quadratic formula will always give you the answer, although that is not the way they want you to solve it.
Quadratic formula:
x = [-5 ± √(5² + 4∙7∙3)]/[2∙7]
= [-5 ± √109]/14
≅ [-5 ± 10.44]/14
≅ -1.10, 0.39
the line has a slope of three for all values of x, so that you'll assume it to be a linear equation interior the form of y = mx + b so we stumble on out what c is by technique of subbing ( 0 , -2) or use (y - y1) = m(x-x1) and we can artwork it out because all of us do not ignore that m(gradient/slope) = 3 both way, we get (y - -2) = 3(x - 0) y + 2 = 3x y = 3x -2 <<<<<<<<<<<<<<<<<