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.

597

step-by-step explanation:

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles