A quadratic function has an axis of symmetry at x=4 and contains the points (2, -6) and (7, -11). Find the equation in standard form (y=ax2+bx+c). Then state the "a" value in the equation.

The equation in standard form is . The "a" value is -1.

Step-by-step explanation:

A quadratic function is the standard form of the parabola. We can take advantage of the symmetry property of the parabola by using the following formula from the Analytical Geometry:

(1)

Where:

- Parabola constant, dimensionless.

- Independent variable, dimensionless.

- Depedent variable, dimensionless.

, - Coordinates of the vertex of the parabola, dimensionless.

If we know that , and , then we have the following system of linear equations:

(2)

(3)

By clearing in (2) and (3) and equalizing each other, we get that:

And the remaining variable is calculated by substituting directly on (3):

Then, the equation of the parabola is:

And the standard form of the equation is obtained by algebraic handling:

(4)

The equation in standard form is . The "a" value is -1.

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step-by-step explanation: