What is 2f(x)=2x^2+3x-4 ?

The solution to 2f(x)=2x^2+3x-4 is Parabola with (h,k)=(-3/4 ,-41/16),p= 1/4

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2f(x)=2x^2+3x-4

2 f (x) = 2 x^{2} + 3 x - 4

(h, k) = (- \frac{3}{4}, - \frac{41}{16}), p = \frac{1}{4}

Solution steps

2 y = 2 x^{2} + 3 x - 4

Rewrite

2 y = 2 x^{2} + 3 x - 4

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{41}{16})) = (x - (- \frac{3}{4}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{3}{4}, - \frac{41}{16}), p = \frac{1}{4}

(x + 2)^{2} = 8 y - 24

2 x = y^{2} + 8 y + 22

- \frac{1}{2 y ^{2}} = - \frac{1}{x}

(x - 3)^{2} = - 8 (y - 0)

x = (y + 5)^{2}

What is 2f(x)=2x^2+3x-4 ?
The solution to 2f(x)=2x^2+3x-4 is Parabola with (h,k)=(-3/4 ,-41/16),p= 1/4