How do you find the vertex of the parabola #y = x^2 – 2x + 4#?

Question

Kennedy Adams · Accepted Answer

Vertex is at #(1,3)# #y=x^2-2x+4 = x^2-2x+1 +3 =(x-1)^2 +3 :. # The vertex is at #(1,3)# graph{x^2-2x+4 [-10, 10, -5, 5]}[Ans]

Jameson Allen · Answer

undefined To find the vertex of the parabola y = x^2 - 2x + 4, you can use the formula x = -b / (2a) where "a" is the coefficient of the x^2 term and "b" is the coefficient of the x term in the equation. In this case, a = 1 and b = -2. Plugging these values into the formula, we get x = -(-2) / (2*1) = 1. Therefore, the x-coordinate of the vertex is 1. To find the corresponding y-coordinate, substitute x = 1 into the equation y = x^2 - 2x + 4. So, y = (1)^2 - 2(1) + 4 = 1 - 2 + 4 = 3. Hence, the vertex of the parabola is (1, 3).

Isaiah Anthony · Answer

undefined To find the vertex of the parabola represented by the equation $ y = x^2 - 2x + 4 $, we use the formula:

$$ x_{\text{vertex}} = -\frac{b}{2a} $$
$$ y_{\text{vertex}} = f(x_{\text{vertex}}) $$

Where $ a $, $ b $, and $ c $ are the coefficients of the quadratic equation in standard form $ ax^2 + bx + c $.

In the given equation $ y = x^2 - 2x + 4 $:
$$ a = 1 $$
$$ b = -2 $$
$$ c = 4 $$

Substituting these values into the formula, we get:
$$ x_{\text{vertex}} = -\frac{-2}{2(1)} = 1 $$

Now, we find the corresponding value of $ y $ by substituting $ x = 1 $ into the equation:
$$ y_{\text{vertex}} = (1)^2 - 2(1) + 4 = 1 - 2 + 4 = 3 $$

Therefore, the vertex of the parabola represented by the equation $ y = x^2 - 2x + 4 $ is $ (1, 3) $.