What is the axis y=x^2+5x+4 ?

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axis y=x^2+5x+4

axis

y = x^{2} + 5 x + 4

x = - \frac{5}{2}

Solution steps

y = x^{2} + 5 x + 4

Rewrite

y = x^{2} + 5 x + 4

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{9}{4})) = (x - (- \frac{5}{2}))^{2}

Therefore parabola properties are:

(h, k) = (- \frac{5}{2}, - \frac{9}{4}), p = \frac{1}{4}

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{5}{2}

y = x^{2} + 7 x - 30

y = x^{2} + 8 x + 16

y = - 5 x^{2} - 40 x - 77

y = 3 x^{2} + 9

\Rightarrow y = 0.5 k x^{2}