What is the equation of the parabola passing through the points(0,6). (3, 15.6), and (10,-4)?
1 answer:
Answer:
y = -0.6x^2 + 5x + 6
Step-by-step explanation:
First, find the equation of a linear line that passes through the points (0,6) and (3, 15.6) in the slope intercept form, y = mx + b. We know that the line has a y-intercept of 6, so b = 6. Substitute 3 for x, 15.6 for y, and 6 for b to find m.
y = mx + b
15.6 = 3m + 6
9.6 = 3m
m = 3.2
y = 3.2x + 6
y = a(x - 0)(x - 3) + 3.2x + 6
y = a(x)(x - 3) + 3.2x + 6
Finally, substitute 10 for x and -4 for y in the equation above to find a.
-4 = a(10)(10 - 3) + 3.2*10 + 6
-4 = a(10)(7) + 32 + 6
-4 = 70a + 38
-42 = 70a
a = -0.6
Simplify to write in standard form.
y = -0.6(x)(x - 3) + 3.2x + 6
y = -0.6x^2 + 5x + 6
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Answer:
The values of x are x = -2 and x= 1.
Step-by-step explanation:
The given equation -x²+4 = x+2 can be written in the form of two functions as
y = -x²+4 which is a function representing parabola and
y = x+2 which is a straight line.
Now we will solve the given equation to find their points of intersection on graph. Their points of intersections will be the answer.
-x²+4 = x+2
-x²+4-x = x+2-x
-x²-x+4 = 2
-x²-x+4-2 = 2-2
-x²-x+2 = 0
Or x²+x-2=0
Now we will factorize the equation.
x²+2x-x-2=0
x(x+2)-1(x+2) = 0
(x+2)(x-1) = 0
x+2 = 0 ⇒x = -2
x-1 = 0 ⇒x = 1
For x = 1, y will be 3
and for x = -2, y will be 0
Now we can see the graph for the given coordinates (-2,0) and (1,3).
