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Dennis_Churaev [7]
2 years ago
11

The vertex of a parabola is (3,2). A second point on the parabola is (1,5).which of the following points is also on the graph?

Mathematics
1 answer:
vekshin12 years ago
8 0
+ <span>The vertex of a parabola is (3,2),
that means the parabola's equation is y=a(x-3)</span>²+2
+ <span>A second point on the parabola is (1,5) and we replace x=1 and y=5. We have: 
5</span>=a(1-3)<span>²+2  ,  so we have 4a=5-2 or a=3/4
So the equation is y=3/4 (x-3)</span>²+2

And by checking we have the point (5;5) is on the parabola
Have fun
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F(x) = -4(x - 2)² + 2
f(x) = -4((x - 2)(x - 2)) + 2
f(x) = -4(x² - 2x - 2x + 4) + 2
f(x) = -4(x² - 4x + 4) + 2
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x = <u>-16 +/- √(16² - 4(-4)(-14))</u>
                       2(-4)
x = <u>-16 +/- √(256 - 224)</u>
                     -8
x = <u>-16 +/- √(32)
</u>               -8<u>
</u>x = <u>-16 +/- 5.66
</u>              -8<u>
</u>x = <u>-16 + 5.66</u>      x = <u>-16 - 5.66
</u>             -8                         -8<u>
</u>x = <u>-10.34</u>            x = <u>-21.66</u>      
          -8                         -8
x = 1.2925           x = 2.7075
f(x) = -4x² + 16x - 14
f(1.2925) = -4(1.2925)² + 16(1.2925) - 14
f(1,2925) = -4(1.67055625) + 20.68 - 14
f(1.2925) = -6.682225 + 20.68 - 14
f(1.2925) = 13.997775 - 14
f(1.2925) = -0.002225
(x, f(x)) = (1.2925, -0.002225)
or
f(x) = -4x² + 16x - 14
f(2.7075) = -4(2.7075)² + 16(2.7075) - 14
f(2.7075) = -4(7.33055625) + 43.32 - 14
f(2.7075) = -29.322225 + 43.32 - 14
f(2.7075) = 13.997775 - 14
f(2.7075) = -0.002225
(x, f(x)) = (2.7075, -0.002225)
--------------------------------------------------------------------------------------------
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f(x) = 2((x - 2)(x - 2)) + 1
f(x) = 2(x² - 2x - 2x + 4) + 1
f(x) = 2(x² - 4x + 4) + 1
f(x) = 2(x²) - 2(4x) + 2(4) + 1
f(x) = 2x² - 8x + 8 + 1
f(x) = 2x² - 8x + 9
2x² - 8x + 9 = 0
x = <u>-(-8) +/- √((-8)² - 4(2)(9))
</u>                      <u />2(2)
x = <u>8 +/- √(64 - 72)</u>
                 4
x = <u>8 +/- √(-8)</u>
             4
x = <u>8 +/- √(8 × (-1))</u>
                 4
x =<u> 8 +/- √(8)√(-1)</u>
                 4
x = <u>8 +/- 2.83i</u>
              4
x = 2 +/- 1.415i
x = 2 + 1.415i      x = 2 - 1.415i
f(x) = 2x² - 8x + 9
f(2 + 1.415i) = 2(2 + 1.415i)² - 8(2 + 1.415i) + 9
f(2 + 1.415i) = 2((2 + 1.415i)(2 + 1.415i)) - 16 - 11.32i + 9
f(2 + 1.415i) = 2(4 + 2.83i + 2.83i + 2.00225i²) - 16 - 11.32i + 9
f(2 + 1.415i) = 2(4 + 5.66i + 2.00225) - 16 - 11.32i + 9
f(2 + 1.415i) = 8 + 11.32i + 4.0045 - 16 - 11.32i + 9
f(2 + 1.415i) = 8 + 4.0045 - 16 + 9 + 11.32i - 11.32i
f(2 + 1.415i) = 12.0045 - 16 + 9
f(2 + 1.415i) = -3.9955 + 9
f(2 + 1.415i) = 5.0045
(x, f(x)) = (2 + 1.415i, 5.0045)
or
f(x) = 2x² - 8x + 9
f(2 - 1.415i) = 2(2 - 1.415i)² - 8(2 - 1.415i) + 9
f(2 - 1.415i) = 2((2 - 1.415i)(2 - 1.415i)) - 16 + 11.32i + 9
f(2 - 1.415i) = 2(4 - 2.83i - 2.83i + 2.00225i²) - 16 + 11.32i + 9
f(2 - 1.415i) = 2(4 - 5.66i + 2.00225) - 16 + 11.32i + 9
f(2 - 1.415i) = 8 - 11.32i + 4.0045 - 16 + 11.32i + 9
f(2 - 1.415i) = 8 + 4.0045 - 16 + 9 - 11.32i + 11.32i
f(2 - 1.415i) = 12.0045 - 16 + 9
f(2 - 1.145i) = -3.9955 + 9
f(2 - 1.415i) = 5.0045
(x, f(x)) = (2 - 1.415i, 5.0045)
--------------------------------------------------------------------------------------------
f(x) = -2(x - 4)² + 8
f(x) = -2((x - 4)(x - 4)) + 8
f(x) = -2(x² - 4x - 4x + 16) + 8
f(x) = -2(x² - 8x + 16) + 8
f(x) = -2(x²) + 2(8x) - 2(16) + 8
f(x) = -2x² + 16x - 32 + 8
f(x) = -2x² + 16x - 24
-2x² + 16x - 24 = 0
x = <u>-16 +/- √(16² - 4(-2)(-24))</u>
                      2(-2)
x = <u>-16 +/- √(256 - 192)</u>
                   -4
x = <u>-16 +/- √(64)</u>
               -4
x = <u>-16 +/- 8</u>
            -4
x = <u>-16 + 8</u>      x = <u>-16 - 8</u>
           -4                   -4
x = <u>-8</u>              x = <u>-24</u>
      -4                     -4
x = 2                x = 6
f(x) = -2x² + 16x - 24
f(2) = -2(2)² + 16(2) - 24
f(2) = -2(4) + 32 - 24
f(2) = -8 + 32 - 24
f(2) = 24 - 24
f(2) = 0
(x,f(x)) = (2, 0)
or
f(x) = -2x² + 16x - 24
f(6) = -2(6)² + 16(6) - 24
f(6) = -2(36) + 96 - 24
f(6) = -72 + 96 - 24
f(6) = 24 - 24
f(6) = 0
(x, f(x)) = (6, 0)
<u />
5 0
3 years ago
Gabriel is a door to door vacuum salesman. His weekly salary, S, is $300 plus $45 for each vacuum he sells. This can be written
lions [1.4K]

Answer:

Gabriel sold 31 vacuums.

Step-by-step explanation:

S = 300 + 45v

1695 = 300 + 45v

1395 = 45v

v = 31

8 0
3 years ago
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