Write the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10).

Step-by-step explanation:

System Of Linear Equations

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

Now we use the second condition f(1)=5

Finally, we use the third condition f(2)=10

We put together eq 1, eq 2, and eq 3 to form the system

Adding the first two equations we have

And also

Using the above equation and the value of b in the third equation, we have

Subtracting the first equation from the second

And therefore

Now we have all the values, the quadratic function is

70

step-by-step explanation:

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b