The equation y = 2x^2 - 8x + 5 represents a parabolic curve. The coefficient of x^2 (2) determines the shape of the graph, while the coefficient of x (-8) determines the slope. The constant term (5) represents the y-intercept, and the vertex of the parabola is (2, -3).
To complete the values of the given equation y = 2x^2 - 8x + 5, we need to determine the missing components of the equation.
Here's how to complete the values step by step:
1. Coefficient of x^2: In the given equation, the coefficient of x^2 is 2. This value tells us how the graph of the equation will be shaped. A positive coefficient means the graph opens upward, while a negative coefficient means the graph opens downward.
2. Coefficient of x: The coefficient of x in the equation is -8. This value determines the slope of the equation. In this case, a negative coefficient indicates that the graph will be slanted downward from left to right.
3. Constant term: The constant term in the equation is +5. This value represents the y-intercept, which is the point where the graph intersects the y-axis. In this case, the graph will intersect the y-axis at the point (0, 5).
4. Quadratic term: The quadratic term, 2x^2, indicates that the equation represents a parabolic curve. The coefficient of the quadratic term affects the shape and steepness of the curve.
To further analyze the equation, we can determine the vertex of the parabola by using the formula: x = -b/2a. In this equation, a represents the coefficient of x^2 (-8) and b represents the coefficient of x (2).
By substituting these values into the formula, we can calculate the x-coordinate of the vertex: x = -(-8) / (2 * 2) = 8 / 4 = 2.
To find the corresponding y-coordinate of the vertex, substitute the x-coordinate into the original equation: y = 2(2)^2 - 8(2) + 5 = 8 - 16 + 5 = -3.
Therefore, the vertex of the parabola is (2, -3).