Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.
y equals x squared minus 10 x minus 4
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Part 1
What is the equation of the axis of​ symmetry?
  
enter your response here ​(Type an equation. Simplify your​ answer.)

Answer 1

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.
y equals x squared minus 10 x minus 4
Question content area bottom
Part 1
What is the equation of the axis of​ symmetry?
  
x equals 5 ​(Type an equation. Simplify your​ answer.)
Part 2
The vertex is
  
enter your response here. ​(Type an ordered​ pair.)

Answer 2

To find the equation of the axis of symmetry, we can use the formula x = -b/(2a) for a quadratic function in the form y = ax^2 + bx + c.

Given the function y = x^2 - 10x - 4, we have a = 1 and b = -10. Plugging these values into the formula, we get:
x = -(-10)/(2*1)
x = 10/2
x = 5

Therefore, the equation of the axis of symmetry is x = 5.

Answer 3

To find the coordinates of the vertex, we substitute the x-coordinate of the axis of symmetry into the function to find the y-coordinate.

When x = 5:
y = 5^2 - 10(5) - 4
y = 25 - 50 - 4
y = -29

Therefore, the coordinates of the vertex are (5, -29).