What is the equation of the quadratic function shown in the graph?

Mathematics

1 answer:

oksano4ka [1.4K]3 years ago

8 0

Answer:

f(x) = x² + 2x - 3

(x+3)(x-1)

Step-by-step explanation:

Zeroes are -3 and 1

Let α = -3 and β = 1

f(x) = x² - (α+β)x + (αβ)

= x² - (-3+1)x + (-3 × 1)

= x² - (-2)x + (-3)

= x² + 2x - 3

x²+2x-3

x² - x + 3x - 3

x(x-1) + 3(x-1)

(x+3)(x-1)

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Solve the system of equations by graphing: 2x + 3y = 2 6x + 18y = 9

cluponka [151]

The answer is A: x=1/2 , y= 1/3

Solve the following system:
{2 x + 3 y = 2 | (equation 1)
{6 x + 18 y = 9 | (equation 2)

Swap equation 1 with equation 2:
{6 x + 18 y = 9 | (equation 1)
{2 x + 3 y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:
{6 x + 18 y = 9 | (equation 1)
{0 x - 3 y = -1 | (equation 2)

Divide equation 1 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x - 3 y = -1 | (equation 2)

Multiply equation 2 by -1:
{2 x + 6 y = 3 | (equation 1)
{0 x+3 y = 1 | (equation 2)

Divide equation 2 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x+y = 1/3 | (equation 2)

Subtract 6 × (equation 2) from equation 1:
{2 x+0 y = 1 | (equation 1)
v0 x+y = 1/3 | (equation 2)

Divide equation 1 by 2:
{x+0 y = 1/2 | (equation 1)
v0 x+y = 1/3 | (equation 2)

Collect results:
Answer: {x = 1/2, y = 1/3