Question

Find the vertex of the parabola y=x^2 + 5x + 10

Answer 1

The coordinates of the vertex of the given parabola $y=x^2+5x+10$ will be $(\dfrac{5}{2},\dfrac{15}{4})$.

What is the vertex of a parabola?

Vertex of the parabola is the point of intersection of symmetry axis of the parabola and the parabola itself.

The given equation of parabola is $y=x^2 + 5x + 10$.

To get the coordinates of vertex of this parabola, we have to write the equation of parabola in the standard form.

So, write the equation of parabola in its standard form as,

$y=x^2 + 5x + 10\\y=x^2+2\times \dfrac{5}{2}x+\dfrac{25}{4}-\dfrac{25}{4}+10\\y=(x-\dfrac{5}{2})^2+\dfrac{15}{4}\\(y-\dfrac{15}{4})=(x-\dfrac{5}{2})^2$

The standard form of parabola is,

$y-b=(x-a)^2$ where (a, b) is the coordinate of the vertex.

So, by comparing the equations, the vertex of the parabola will be $(\dfrac{5}{2},\dfrac{15}{4})$.

Therefore, the coordinates of the vertex of the given parabola $y=x^2+5x+10$ will be $(\dfrac{5}{2},\dfrac{15}{4})$.

Learn more about vertex of parabola here:

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