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What is the y coordinate of the vertex of a parabola #y=x^2-6x+14#?

Answer 1

The vertex's y coordinate would be 5.

By completing the square of the terms that contain x, first write the equation in standard form.

y= #x^2# -6x +9 +5 = #(x -3)^2# +5. Having done this the vertex of the parabola is is given by x-3=0, that is x=3 and y=5. Hence y coordinate is 5.

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Answer 2

Jameson Allen

The y-coordinate of the vertex of the parabola ( y = x^2 - 6x + 14 ) can be found using the formula for the x-coordinate of the vertex, which is ( x = -\frac{b}{2a} ), where ( a ) and ( b ) are the coefficients of the quadratic equation ( y = ax^2 + bx + c ). In this case, ( a = 1 ) and ( b = -6 ).

Substituting these values into the formula, we get:

[ x = -\frac{-6}{2 \cdot 1} = \frac{6}{2} = 3 ]

To find the y-coordinate corresponding to this x-coordinate, we plug ( x = 3 ) into the equation ( y = x^2 - 6x + 14 ):

[ y = (3)^2 - 6(3) + 14 ] [ y = 9 - 18 + 14 ] [ y = 5 ]

So, the y-coordinate of the vertex is ( y = 5 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.