What is the equation, in standard form, of a parabola that contains the following points? (-2, 18), (0, 4), (4, 24)
y = 2x² - 3x + 4
y = -3x² + 2x + 4
y = -4x² - 3x - 2
y = -2x² + 3x - 4 

Solution:

The standard form of the parabola is y = ax² + bx + c

As it passess through (-2, 18), (0, 4), (4, 24), each of these points satisfies the equation of the parabola.

Substitute (-2, 18) in standard form of parabola, we get

18 = a (-2)² + b (-2) + c

18 = 4a - 2b + c --- (1)

Substitute (0, 4) in standard form, we get

4 = c --- (2)

Substitute (4, 24) in standard form, we get

24 = a(4)² + b(4) + c

24 = 16a + 4b + c --- (3)

Multiply equation (1) by 4

72 = 16a - 8b + 4c --- (4)

24 = 16a + 4b + c

Subtract both the equations (4) and (3)

48 = -12b + 3c

Substitute equation (2) c = 4, we get

48 = -12b + 3(4)

48 = -12b + 12

-12b = 48 - 12

-12b = 36

Divide both sides by -12

b = -3

Substitute the value of b = -3 in equation (1)

18 = 4a - 2(-3) + 4

18 = 4a + 6 + 4

4a = 18 - 6 - 4

4a = 8

Divide both sides by 4

a = 2

Therefore, the equation in standard form is y = 2x² - 3x + 4.

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What is the equation, in standard form, of a parabola that contains the following points? (-2, 18), (0, 4), (4, 24)

Summary:

The equation, in standard form, of a parabola that contains the following points (-2, 18), (0, 4), (4, 24) is y = 2x² - 3x + 4.