Find the coordinates of the vertex for the parabola defined by the given quadratic function f(x)= x² - 4x + 10.

Solution:

We have to find the coordinates of the vertex for the parabola.

For any equation of the type y = ax² + bx + c, the vertex is given by (h,k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Given, the equation is y = x² - 4x + 10

Here, a = 1, b = -4 and c = 10

So, h = -(-4)/2(1)

h = 4/2

h = 2

4ac = 4(1)(10)

4ac = 40

So, k = [40 - (-4)²]/4(1)

k = (40 - 16)/4

k = 24/4

k = 6

Therefore, the coordinates of the vertex is (h,k) = (2, 6).

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Find the coordinates of the vertex for the parabola defined by the given quadratic function f(x)= x² - 4x + 10.

Summary:

The coordinates of the vertex for f(x) = x² - 4x + 10 are (2, 6).