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The statements about the function that are true are
- The vertex of the function is at (–3,–16).
- The graph is increasing on the interval x > –3.
- The graph is positive only on the intervals where x < –7 and where x > 1.
The equation of the graph is given as
f(x) = (x - 1)(x + 7)
The graph of the function is added as an attachment
On the graph, we have
Vertex = (-3, -16)
This is so because the graph has a minimum point of (-3, -16)
Also, the graph crosses the x-axis at x = 1 and x = -7
This means that the graph is positive at x >1 and x >-7
Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3
Read more about quadratic functions at
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3x-2y=6
1) <span>Add -3x to both sides.
</span><span><span> 3x</span>−<span>2y</span></span>=<span>6
</span>+3x +3x
-----------------
<span>−<span>2y</span></span>=<span><span>−<span>3x</span></span>+<span>6
</span></span><span>
2) Divide both sides by -2.
</span>
= 
y=<span><span><span>32</span>x</span>−<span>3
</span></span>
3) Substitute the y with the equation
3x-2(32x-3)=6
3x-64x+6=6
4) Combine like terms
3x-64x+6=6
-61x+6=6
5) Subtract 6 from each side of the equation
-61x+6=6
-6 -6 (+6-5 gets crossed out)
--------------
-61x=0
6) Divide both sides by -61
x=0
============================================================
Now that you've got you x intercept, use the x value and substitute it into the
y=32x−3
y=32(0)-3
y=0-3
y=-3
(0,-3)
1) <span>Add -3x to both sides.
</span><span><span> 3x</span>−<span>2y</span></span>=<span>6
</span>+3x +3x
-----------------
<span>−<span>2y</span></span>=<span><span>−<span>3x</span></span>+<span>6
</span></span><span>
2) Divide both sides by -2.
</span>
y=<span><span><span>32</span>x</span>−<span>3
</span></span>
3) Substitute the y with the equation
3x-2(32x-3)=6
3x-64x+6=6
4) Combine like terms
3x-64x+6=6
-61x+6=6
5) Subtract 6 from each side of the equation
-61x+6=6
-6 -6 (+6-5 gets crossed out)
--------------
-61x=0
6) Divide both sides by -61
x=0
============================================================
Now that you've got you x intercept, use the x value and substitute it into the
y=32x−3
y=32(0)-3
y=0-3
y=-3
(0,-3)