Write the equation of the quadratic function whose graph is shown. Use the formula y=a(x-h)^2+k

Question

Points are (4,7) and (6,3)

Answer 1

The given points lie on the same graph.  We can use the given points and the formula to write a system of equations.

 

 

The equation when the point is  (4, 7) is plugged into the formula is

 

7 = a(4 - h)² + k

7 = a(16 - 8h + h²) + k

7 = 16a - 8ah + ah² + k

 

 

The equation when the point is (6, 3) is plugged into the formula is

 

3 = a(6 - h)² + k

3 = a(36 - 12h + h²) + k

3 = 36a - 12ah + ah² + k

 

 

We have two equations to work with.

 

7 = 16a - 8ah + ah² + k           eq1

 

3 = 36a - 12ah + ah² + k          eq2

 

 

We can subtract eq2 from eq1 to eliminate the last two terms  ah²+k.

 

4 = -20a + 4ah

 

 

4 = 4a(-5 + h)

 

 

Divide both sides of the equation by 4.

 

1 = a(-5 + h)

 

 

Let     a=1      so that   h = 6

 

 

Next, we can plug in these values into the original eq2 to find k.

 

3 = a(6 - h)² + k

3 = 1(6 - 6) + k

3 = 0 + k

3 = k

 

 

The function we want is

 

y = (x - 6)² + 3