What is the axis y=(2x+3)^2 ?

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axis y=(2x+3)^2

axis

y = (2 x + 3)^{2}

x = - \frac{3}{2}

Solution steps

y = (2 x + 3)^{2}

Rewrite

y = (2 x + 3)^{2}

in the standard form:

4 \cdot \frac{1}{16} (y - 0) = (x - (- \frac{3}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{3}{2}, 0), p = \frac{1}{16}

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}{2}

y = - \frac{1}{4} (x + 9)^{2} - 7

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

y^{2} = 5 x + 3

(y + 4)^{2} = 7 (x - 2)

y = 6 x^{2} + 3 x