Quadratic function

Write the equation of the quadratic function, which includes points A (-1, 10), B (2, 19), C (1,4)

Correct answer:

a = 6
b = -3
c = 1

Step-by-step explanation:

f (x) = a x^{2} + b x + c A = (- 1, 10) B = (2, 19) C = (1, 4) a \cdot A_{x}^{2} + b \cdot A_{x} + c = A_{y} a \cdot B_{x}^{2} + b \cdot B_{x} + c = B_{y} a \cdot C_{x}^{2} + b \cdot C_{x} + c = C_{y} a \cdot (- 1)^{2} + b \cdot (- 1) + c = 10 a \cdot 2^{2} + b \cdot 2 + c = 19 a \cdot 1^{2} + b \cdot 1 + c = 4 a - b + c = 10 4 a + 2 b + c = 19 a + b + c = 4 P i v o t : R o w 1 \leftrightarrow R o w 2 4 a + 2 b + c = 19 a - b + c = 10 a + b + c = 4 R o w 2 - \frac{1}{4} \cdot R o w 1 \to R o w 2 4 a + 2 b + c = 19 - 1.5 b + 0.75 c = 5.25 a + b + c = 4 R o w 3 - \frac{1}{4} \cdot R o w 1 \to R o w 3 4 a + 2 b + c = 19 - 1.5 b + 0.75 c = 5.25 0.5 b + 0.75 c = - 0.75 R o w 3 - \frac{0 . 5}{- 1 . 5} \cdot R o w 2 \to R o w 3 4 a + 2 b + c = 19 - 1.5 b + 0.75 c = 5.25 c = 1 c = \frac{1}{1} = 1 b = \frac{5 . 2 5 - 0 . 7 5 c}{- 1 . 5} = \frac{5 . 2 5 - 0 . 7 5 \cdot 1}{- 1 . 5} = - 3 a = \frac{1 9 - 2 b - c}{4} = \frac{1 9 - 2 \cdot ( - 3 ) - 1}{4} = 6 a = 6 b = - 3 c = 1 f (x) = a x^{2} + b x + c f (x) = 6 x^{2} - 3 x + 1

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators

Are you looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?

You need to know the following knowledge to solve this word math problem:

Grade of the word problem:

high school

Related math problems and questions: