Find the equation of the parabola that passes through the points:
(0,5) (1,7) and (-2,19)

The equation of the parabola is:

Step-by-step explanation:

The standard form of a parabola is given as:

The three points on the parabola are (0,5), (1,7), and (-2,19).

Plug in the three points and find three equations in a,b and c

Using point (0,5) in the equation, we get

Using point (1,7) in the equation, we get

Using point (-2,19) in the equation, we get

Plug in the value of c=5 in the last two equations. This gives,

Now, add the two new equations. This gives,

Now, plug in in equation 4 gives,

Therefore, the equation of the parabola is:

step-by-step explanation:

step-by-step explanation: