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vazorg [7]
2 years ago
8

Please help and explain.

Mathematics
1 answer:
Radda [10]2 years ago
7 0

Explanation:

Vertex form of a quadratic function is given by y = a(x - h)² + k

where

1) 'a' determines if parabola is stretched or compressed.

   If a > 1 then graph is stretched by a factor of a.

   If 0 < a < 1, then graph is compressed by a factor of a.

2) If a > 0 then graph opens upwards with a happy face. (minimum)

3) If a < 0 then graph opens downwards with a sad face. (maximum)

4) (h, k) is the vertex point

5) The axis of symmetry is x = h

While solving for y = 1(x - 4)² + 3

Identify following's:

Vertex: (h, k) = (4, 3)

Axis of symmetry: x = 4

Max/Min: As here a > 0, Minimum (4, 3)

Stretch/compression: a = 1, the graph is stretched by a factor of 1.

Direction of opening: As a > 0, the graph opens upwards.

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Read 2 more answers
2/3x + 1/6 = -3/4x + 1
kupik [55]
\frac{2}{3} x +  \frac{1}{6}  =  -\frac{3}{4} x + 1

First, simplify \frac{2}{3} x to \frac{2x}{3} / Your problem should look like: \frac{2x}{3} +  \frac{1}{6} =  -\frac{3}{4} x + 1
Second, simplify \frac{3}{4} x to \frac{3x}{4} / Your problem should look like: \frac{2x}{3} +  \frac{1}{6} =  -\frac{3x}{4} + 1
Third, multiply both sides by 12 (the LCM of 3 and 4) / Your problem should look like: 8x + 2 = -9x + 12
Fourth, subtract 2 from both sides. / Your problem should look like: 8x = -9x + 12 - 2
Fifth, simplify -9x + 12 - 2 to -9x + 10. / Your problem should look like: 8x = -9x + 10
Sixth, add 9x to both sides. / Your problem should look like: 8x + 9x = 10
Seventh, add 8x + 9x to get 17x. / Your problem should look like: 17x = 10
Eighth, divide both sides by 17. / Your problem should look like: x =  \frac{10}{17}

Answer as fraction: x = \frac{10}{17}
Answer as decimal: x = 0.5882

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