The quadratic function f(x) = 2·x² + 6·x + 7, indicates that the parameters of the graph of the function are;
(a) (-1.5, 2.5)
(b) x = -1.5
(c) Minimum value
(d) Please find attached the graph of the function f(x) = 2·x² + 6·x + 7, created with MS Excel
What is a quadratic function?; A quadratic function is a function of the form f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c, are numbers
The x-coordinate of the vertex can be found using the equation;
x-coordinate of vertex = -b/(2·a)
Therefore; x-coordinate of vertex = -6/(2×2)
-6/(2×2) = -3/2
-3/2 = -1.5
The y-coordinate of the vertex is therefore;
f(-1.5) = 2 × (-1.5)² + 6 × (-1.5) + 7
2 × (-1.5)² + 6 × (-1.5) + 7 = 2.5
The y-coordinate of the vertex is; y = 2.5
The vertex is therefore; (-1.5, 2.5)
(b) The axis of symmetry of the quadratic equation of the form; f(x) = 2·x² + 6·x + 7 is the equation x = x-coordinate of the vertex, therefore;
The axis of symmetry is; x = -1.5
(c) The quadratic function f(x) = 2·x² + 6·x + 7, with a positive leading coefficient has a ∪ shape, and therefore has a minimum point
(d) The graph of the function, f(x) = 2·x² + 6·x + 7 can be obtained by calculating the values in the ordered pair and plotting the values on the coordinate plane as follows;
x; -6, -5, -4, -3, -2, -1, 0, 1, 2, 3
y; 43, 27, 15, 7, 3, 3, 7, 15, 27, 43
The above points points can be used to plot the graph of the function f(x) = 2·x² + 6·x + 7 using MS Excel