What is the minimum point of the graph of the equation y=2x^(2) + 8x +9?
(-2 1)
To draw the graph of 2×+8×+9
To find the minimum point of the graph of the equation y = 2x^2 + 8x + 9, we need to determine the vertex of the parabola.
The equation is in the form y = ax^2 + bx + c, where a = 2, b = 8, and c = 9.
The x-coordinate of the vertex can be found using the formula x = -b / (2a).
Substituting the values, we have x = -8 / (2 * 2) = -8 / 4 = -2.
To find the y-coordinate of the vertex, substitute the x-value (-2) back into the equation.
y = 2(-2)^2 + 8(-2) + 9
y = 2(4) - 16 + 9
y = 8 - 16 + 9
y = 1.
Therefore, the minimum point of the graph is (-2, 1).
To find the minimum point of the graph of the equation y = 2x^2 + 8x + 9, we can use the concept of the vertex of a quadratic function.
The vertex of a quadratic function in the form y = ax^2 + bx + c is given by the coordinates (h, k), where h = -b/2a and k is the minimum (or maximum) value of the function.
In our case, the equation y = 2x^2 + 8x + 9 is already in the form y = ax^2 + bx + c, where a = 2, b = 8, and c = 9.
To find the x-coordinate of the vertex, we can use the formula h = -b/2a:
h = -8/(2*2) = -8/4 = -2
Now, substitute this value of h into the equation to find the y-coordinate:
k = 2*(-2)^2 + 8*(-2) + 9 = 2*4 - 16 + 9 = 8 - 16 + 9 = 1
Therefore, the minimum point of the graph of the equation y = 2x^2 + 8x + 9 is (-2, 1).