4 years ago

Which statements are true about the x-intercepts of quadratic functions?

Mathematics

1 answer:

oksano4ka [1.4K]4 years ago

8 0

Answer:

A quadratic function can have up to two x-intercepts.

An x-intercept of a quadratic function is also called a zero of the function.

Step-by-step explanation:

None needed.

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4 years ago

Sin(x+2y)=cos(2x -y)

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$~~~~~~~\sin (x+2y) = \cos (2x-y)\\\\\\\implies \dfrac{d}{dx} \sin(x+2y) = \dfrac{d}{dx} \cos (2x-y)\\\\\\\implies \cos(x+2y)\dfrac{d}{dx}(x+2y) = -\sin(2x-y) \dfrac{d}{dx}(2x-y)~~~~~~~~~~~;[\text{Chain rule}]\\\\\\\implies \cos(x+2y) \left(1+2 \dfrac{dy}{dx}\right) = -\sin(2x-y)\left(2-\dfrac{dy}{dx} \right)\\\\\\\implies \cos(x+2y) + 2\cos(x+2y)\dfrac{dy}{dx} = -2\sin(2x-y)+\sin(2x-y) \dfrac{dy}{dx}\\ \\\\$

$\implies \sin(2x-y) \dfrac{dy}{dx} - 2\cos(x+2y) \dfrac{dy}{dx} = \cos(x+2y) + 2\sin (2x-y)\\\\\\\implies \left[\sin(2x-y) -2\cos(x+2y) \right] \dfrac{dy}{dx} = \cos(x+2y) + 2\sin (2x-y)\\\\\\\implies \dfrac{dy}{dx} = \dfrac{\cos(x+2y) + 2\sin (2x-y)}{\sin(2x-y) -2\cos(x+2y) }$