Finding Quadratic Function from Vertex and Leading Coefficient

TLDR; Finding a quadratic function given the vertex and leading coefficient. Using the vertex coordinates and axis of symmetry to solve for the values of B and C.

🔍 Determining B and C

The problem involves determining the values of B and C for a quadratic function with a given vertex and leading coefficient.

The vertex has an X coordinate of 3 and a Y coordinate of -17, with the leading coefficient (A) being -2.

The task is to find the values of B and C for the quadratic function based on this information.

📈 Axis of Symmetry

The equation for the axis of symmetry of a quadratic function, when written in general form, is X = -B/2A.

The X coordinate of the vertex is determined using this equation, and it is the same formula used to find the equation of the axis of symmetry.

The Y coordinate of the vertex, being on the function, must be F of -B/2A.

🔢 Using the Axis of Symmetry

Starting with the equation of the axis of symmetry, which gives the X coordinate of the vertex as 3.

By substituting the known values, such as A being -2, the equation -B/2A = 3 is used to solve for the value of B.

After calculations, it is found that B = 12.

🧮 Solving for C

When X = 3 and Y = -17, the function F of 3 must equal -17.

By substituting the value of B (which is 12) into the function, the equation is formed as -2*3^2 + 12*3 + C = -17.

Solving for C yields C = -35.

📝 Quadratic Function

With B = 12 and C = -35, the quadratic function is determined to be F of X = -2X^2 + 12X - 35.

This function satisfies the given conditions of the vertex and leading coefficient.