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3 years ago

Please help! Quadratic equations!

Mathematics

1 answer:

Alexeev081 [22]3 years ago

7 0

Answer:

$x^2 -2x - 35 =0$

Step-by-step explanation:

Assume that the quadratic term of this equation has no coefficient. One can set the equation up in factored form using the given roots. Then expand the equation and simplify the equation to convert to standard form.

The equation in factored form is the following,

$(x+5)(x-7)=0$

Expand, multiply every term in one of the parenthesis by every term in the other,

$(x+5)(x-7)=0\\\\(x)(x)+(5)(x)-(7)(x)+(-7)(5)=0$

Simplify,

$x^2 +5x -7x -35 =0\\\\x^2 -2x -35=0$

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The reciprocal parent function is translated 5 units right and 3 units up. Write an equation to represent the new function.

ladessa [460]

Answer:

The new function is $y=\frac{1}{x-5}+3$ , where x ≠ 5

Step-by-step explanation:

The reciprocal parent function is $f(x)=\frac{1}{x}$ , where x ≠ 0

The translation of f(x) to the right h units is f(x - h)

The translation of f(x) up k units is f(x) + k

The translation of f(x) to the right h units and up k units is f(x - h) + k

∵ The equation of the reciprocal parent function is $y=\frac{1}{x}$

∵ The function is translated 5 units right

∴ h = 5

- That means 5 is subtracted from x ⇒ (x - 5)

∵ The function is translated 3 units up

∴ k = 3

- That means y added by 3

∴ $y=\frac{1}{x-5}+3$

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___________________

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Step-by-step explanation:

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