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krypsojx

Answered question

2021-12-04

Write the equation of the quadratic function whose graph is a parabola containing the given points
1.

(0, 1), (3, 10), and (- 2, 15)

George Burge

Beginner2021-12-05Added 16 answers

Step 1
Let the equation of the quadratic function be:

f (x) = y = a x_{d x}^{2} + c

This function passes through the points (0,1),(3,10) and (-2,15).
Then we get,

a {(0)}^{2} + b (0) + c = 1

\Rightarrow 0 + 0 + c = 1

\Rightarrow c = 1

Also we get,

a {(3)}^{2} + b (3) + c = 10

\Rightarrow 9 a + 3 b + c = 10

\Rightarrow 9 a + 3 b + 1 = 10

\Rightarrow 9 a + 3 b = 10 - 1

\Rightarrow 9 a + 3 b = 9

\Rightarrow 3 a + b = 3

Moreover,

a {(- 2)}^{2} + b (- 2) + c = 15

\Rightarrow 4 a - 2 b + c = 15

\Rightarrow 4 a - 2 b + 1 = 15

\Rightarrow 4 a - 2 b = 15 - 1

\Rightarrow 4 a - 2 b = 14

\Rightarrow 2 a - b = 7

Step2
Thus we get following two equations in a and b:

3 a + b = 3

2 a - b = 7

Solving we get,

5 a = 10

a = \frac{10}{5} = 2

and

b = 3 - 3 a = 3 - 3 (2) = 3 - 6 = - 3

Therefore we get,

a = 2; b = - 3; c = 1

Hence the required quadratic function will be:

f (x) = 2 x^{2} - 3 x + 1

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