What is the line of symmetry for the parabola whose equation is y = x² + 10x + 25?

Solution:

Given parabola equation y = x² + 10x + 25

Clearly, we can see that the equation contains x² it means it is symmetric to y axis

It can be written as y = (x + 5)²

The vertex means the point which touches the x-axis

At x-axis, we know that y = 0

Now to find vertex, equate (x + 5)² to 0

⇒ (x + 5)² = 0

⇒ (x + 5) = 0

⇒ x= -5

So, the vertex is at (-5, 0)

The line of symmetry means the line which divides the parabola into two equal halves.

So, the x-coordinate is fixed and y-coordinates can be any point on the line.

Therefore, the line of symmetry is x = -5

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What is the line of symmetry for the parabola whose equation is y = x² + 10x + 25?

Summary:

The line of symmetry for the parabola whose equation is y = x² + 10x + 25 is x = -5.