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.)
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.
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.)
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).