Step 1: Identify the standard form of the parabola's equation. From the previous problem, the equation of the parabola is (y−4)² = 4(x−4). This equation is in the standard form for a horizontal parabola: (y−k)² = 4p(x−h). Step 2: Extract the coordinates of the vertex (h,k) by comparing the given equation with the standard form. Comparing (y−4)² = 4(x−4) with (y−k)² = 4p(x−h): We can see that h=4 and k=4. The vertex of the parabola is (h,k) = (4,4). The vertex is (4,4).

Calculate the vertex

July 4, 2026Mathematics

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Answer

(4,4)

Step-by-step solution

2 steps

Identify the standard form of the parabola's equation.
From the previous problem, the equation of the parabola is $(y-4)^2 = 4(x-4)$ .
This equation is in the standard form for a horizontal parabola: $(y-k)^2 = 4p(x-h)$ .
Extract the coordinates of the vertex $(h,k)$ by comparing the given equation with the standard form.
Comparing $(y-4)^2 = 4(x-4)$ with $(y-k)^2 = 4p(x-h)$ :
We can see that $h=4$ and $k=4$ .

The vertex of the parabola is $(h,k) = (4,4)$ .

The vertex is $(4,4)$ .

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Calculate the vertex

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Step-by-step solution

Identify the standard form of the parabola's equation.

Extract the coordinates of the vertex $(h,k)$ by comparing the given equation with the standard form.

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