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3 years ago

The team first experiments with changing the position of the curved pit. In the computer program, the

Mathematics

1 answer:

Tju [1.3M]3 years ago

6 0

Answer:

1). Shifted 2 units right.

2). Shifted 2 units left.

3). Shifted 2 units up.

4). Shifted 2 units down.

Step-by-step explanation:

Parent quadratic function is,

y = x²

1). When curved pit of the parent function is shifted 2 units right,

Translated function will be,

y = (x - 2)²

2). The curved pit is shifted 2 units left,

y = (x + 2)²

3). The curved pit is shifted 2 units up,

y = x² + 2

4). The curved pit is shifted 2 units down,

y = x² - 2

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3 years ago

A parabola can be drawn given a focus of

Volgvan

Answer:

$y=-\frac{1}{4}(x-2)^{2}+9$

Step-by-step explanation:

Any point on a given parabola is equidistant from focus and directrix.

Given:

Focus of the parabola is at $(2,8)$ .

Directrix of the parabola is $y=10$ .

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Therefore,

$\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|$

Squaring both sides, we get

$(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9$