6x^2=-19x-15 solve the equation by graphing and at most two decimal places
1 answer:
Answer:
Step-by-step explanation:
If you are going to graph this, then you should get everything to one side and equate the empty side to y
y = 6x^2 + 19x + 15
The graph is below.
You could use the quadratic equation on this, but it does factor, although not easily.
y = (3x + 5 )(2x + 3)
the roots are found by equating the two binomial factors to 0, each in turn.
3x + 5 = 0 Binomial factor number one. equate to 0
3x = - 5 Subtract 5 from both sides
3x/3 = - 5/3 Divide by 3
x = - 1.667 or
x = - 1.67
2x + 3 = 0 Binomial factor number two. equate to 0
2x = - 3 Subtract 3 from both sides
2x/2 = -3/2
x = - 1.5
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The function f(x) is vertically compressed to form g(x) while the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
<h3>How to compare both functions?</h3>The functions are given as
f(x) =x^2
g(x) =3x^2
h(x) = -3x^2
Substitute f(x) =x^2 in g(x) =3x^2 and h(x) = -3x^2
g(x) =3f(x)
h(x) = -3f(x)
This means that the function f(x) is vertically compressed to form g(x)
Also, the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
See attachment for the functions g(x) and h(x)
Also, functions f(x) and g(x) have the same domain and range
While functions f(x) and h(x) have the same domain but different range
The complete table is:
x -2 -1 0 1 2
g(x) 12 3 0 3 12
h(x) -12 -3 0 -3 -12
Read more about function transformation at:
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