Help please. Question is in picture.
2 answers:
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Answer:
Answers are in bold
Step-by-step explanation:
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<u>Part 1A</u>
Use the Zero Product Property to find the x-intercepts:
0=-(x+4)(x-1)
0=(x+4)(x-1)
0=(x+4)
-4=x
x=-4
0=(x-1)
1=x
x=1
So the x-intercepts are x=-4 and x=1 which is also (-4,0) and (1,0)
For the y-intercepts, plug in x=0:
f(x)=-(0+4)(0-1)
f(x)=(-4)(-1)
f(x)=4
So the y-intercept is y=4 which is also (0,4)
<u>Part 1B</u>
In general, the axis of symmetry is equal to x=h in the equation y=(x-h)^2+k
For a parabola, the axis of symmetry is equal to x=-b/2a, so we expand the given equation and then plug in the values of "a" and "b" to get the axis of symmetry:
f(x)=-(x+4)(x-1)
f(x)=-(x^2+3x-4)
f(x)=-x^2-3x+4
So now we know a=-1 and b=-3, therefore we can plug them in:
x=-b/2a
x=-(-3)/2(-1)
x=3/-2
x=-3/2
x=-1.5
So the equation of the axis of symmetry is x=-1.5
<u>Part 1C</u>
We'll use the equation x=-b/2a to get the x-coordinate for the vertex (which we already know is x=-1.5), then plug in that value of x in the original equation to get the y-coordinate for the vertex:
f(x)=-(-1.5+4)(-1.5+1)
f(x)=-(2.5)(-0.5)
f(x)=-(-1.25)
f(x)=1.25 <-- y-coordinate
So the coordinates of the vertex are (-1.5,1.25)
<u>Part 1D</u>
See the image below
I'll let someone else do the last 4 questions as I am unable to answer them.
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Hey there! :)
Answer:
㏒ (1/25) = -2.
Step-by-step explanation:
Starting with:
㏒ (1/25) =
We can rewrite this expression as:
1/25 is equivalent to , therefore:
x = -2.
Therefore, ㏒ (1/25) = -2.
Well hmmm does the graph open upwards or downwards? well
is a quadratic, if the leading term's coefficient is negative, Down, if positive, Up
a)
now, let's see the leading term, -x², what's its coefficient? is -1 * x² or -1x², is -1, so is negative, thus is opening downwards
c)
x-intercepts occur, when y = 0, namely y = -x²-4x-3, so setting y to 0
0 = -x² -4x -3 take a common factor of -1, thus
0 = -1 (x²+4x+3) <--- now, if we factor that out, notice, surely you've done many of these by now, so we end up with
so, the x-intercepts are at -3 and -1
d)
now, the y-intercepts, just set x = 0
y = -x²-4x-3, settting x to 0 y = -0²-4(0)-3, which is y = -3
so the sole y-intercept is at y = -3
now, let's get on to b)
b)
and those are the coordinates, notice a = -1, b = -4 and c = -3
now, for
e)
well, all you have to do is, once you have the vertex, pick an x-value on the left-hand-side of the vertex, get they value for "y", or OUTPUT,
then pick another x-value, on the right-hand-side of the vertex, get the "y" value again, and plot away
is a quadratic, if the leading term's coefficient is negative, Down, if positive, Up
a)
now, let's see the leading term, -x², what's its coefficient? is -1 * x² or -1x², is -1, so is negative, thus is opening downwards
c)
x-intercepts occur, when y = 0, namely y = -x²-4x-3, so setting y to 0
0 = -x² -4x -3 take a common factor of -1, thus
0 = -1 (x²+4x+3) <--- now, if we factor that out, notice, surely you've done many of these by now, so we end up with
so, the x-intercepts are at -3 and -1
d)
now, the y-intercepts, just set x = 0
y = -x²-4x-3, settting x to 0 y = -0²-4(0)-3, which is y = -3
so the sole y-intercept is at y = -3
now, let's get on to b)
b)
and those are the coordinates, notice a = -1, b = -4 and c = -3
now, for
e)
well, all you have to do is, once you have the vertex, pick an x-value on the left-hand-side of the vertex, get they value for "y", or OUTPUT,
then pick another x-value, on the right-hand-side of the vertex, get the "y" value again, and plot away