Determine a and k so the given points are on the graph of the function.
1 answer:
Answer:
y = -7(x +1)² +35
Step-by-step explanation:
The given quadratic equation has two parameters you are asked to find. When you fill in the given point values, the result is two linear equations in the two unknown parameters. You can solve these equations in any of the usual ways.
__
<h3>equation for point (1, 7)</h3>y = a(x +1)² +k
7 = a(1 +1)² +k
7 = 4a +k
<h3>equation for point (2, -28)</h3>-28 = a(2 +1)² +k
-28 = 9a +k
<h3>solution</h3>The first equation can be subtracted from the second equation to eliminate the k variable. (This is solving by <em>elimination</em>.)
(-28) -(7) = (9a +k) -(4a +k)
-35 = 5a . . . . . . . . simplify
-7 = a . . . . . . . . divide by 5
Using the first equation, we can find k.
7 -4a = k . . . . . subtract 4a
7 -4(-7) = k . . . . substitute for 'a'
35 = k
The parameter values are a = -7, and k = 35. The quadratic equation is ...
y = -7(x +1)² +35
You might be interested in
It is nonequivalent. Figure it out this way. Think about what number has to be multiplied by both the numerator and the denominator of to get to
. It has to be the samee number for the one expression to be equivalent to the other. To get from 5x to x^3, we have to multiply by 1/5x^2. When we do that we get x^3. Good. Now we have to multiply the denominator by the same thing, 1/5x^2.
. As you can see, they are not equivalent.