Question: Identify the coordinates of the vertex of the parabola created by graphing the equation $y = 2x^2 - 12x + 10$. Then, identify if the vertex is a minimum or a maximum.
x-coordinate= Enter answer
y-coordinate= Enter answer
Vertex (Minimum or maximum): Enter answer
1. **State the problem:** We need to find the vertex of the parabola given by the equation $$y = 2x^2 - 12x + 10$$ and determine if the vertex is a minimum or maximum.
2. **Recall the vertex formula:** For a quadratic equation in the form $$y = ax^2 + bx + c$$, the x-coordinate of the vertex is given by $$x = -\frac{b}{2a}$$.
3. **Identify coefficients:** Here, $$a = 2$$, $$b = -12$$, and $$c = 10$$.
4. **Calculate the x-coordinate of the vertex:**
$$x = -\frac{-12}{2 \times 2} = \frac{12}{4} = 3$$
5. **Calculate the y-coordinate by substituting $$x=3$$ back into the equation:**
$$y = 2(3)^2 - 12(3) + 10 = 2 \times 9 - 36 + 10 = 18 - 36 + 10 = -8$$
6. **Determine if the vertex is a minimum or maximum:** Since $$a = 2 > 0$$, the parabola opens upwards, so the vertex is a minimum point.
**Final answer:**
- x-coordinate = $3$
- y-coordinate = $-8$
- Vertex is a minimum point.