What is the axis y=2x^2-3x ?

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axis y=2x^2-3x

axis

y = 2 x^{2} - 3 x

x = \frac{3}{4}

Solution steps

y = 2 x^{2} - 3 x

Rewrite

y = 2 x^{2} - 3 x

in the standard form

4 \cdot \frac{1}{8} (y - (- \frac{9}{8})) = (x - \frac{3}{4})^{2}

Therefore parabola properties are:

(h, k) = (\frac{3}{4}, - \frac{9}{8}), p = \frac{1}{8}

Parabola is of the form

4 p (y - k) = (x - h)^{2}

and is symmetric around the

y

-axis

Axis of symmetry is a line parallel to the

y

-axis which intersects the vertex:

x = \frac{3}{4}

y = 3 x^{2} - 6 x - 24

y = 4 x^{2} + 8 x + 13

16 x^{2} - 72 x - 112 y = - 221

x = (4 y + 3) (2 y - 5)

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