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2 years ago

Can someone answer question 2a and b only please

Mathematics

1 answer:

Mice21 [21]2 years ago

8 0

Answer:

2a) -2

b) 8

Step-by-step explanation:

Equation of a parabola in vertex form

f(x) = a(x - h)² + k

where (h, k) is the vertex and the axis of symmetry is x = h

2 a)

Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):

f(x) = a(x - 2)² - 6

If one of the x-axis intercepts is 6, then

f(6) = 0

⇒ a(6 - 2)² - 6 = 0

⇒ 16a - 6 = 0

⇒ 16a = 6

⇒ a = 6/16 = 3/8

So f(x) = 3/8(x - 2)² - 6

To find the other intercept, set f(x) = 0 and solve for x:

f(x) = 0

⇒ 3/8(x - 2)² - 6 = 0

⇒ 3/8(x - 2)² = 6

⇒ (x - 2)² = 16

⇒ x - 2 = ±4

⇒ x = 6, -2

Therefore, the other x-axis intercept is -2

Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):

f(x) = a(x - 2)² - 6

If one of the x-axis intercepts is -4, then

f(-4) = 0

⇒ a(-4 - 2)² - 6 = 0

⇒ 36a - 6 = 0

⇒ 36a = 6

⇒ a = 6/36 = 1/6

So f(x) = 1/6(x - 2)² - 6

To find the other intercept, set f(x) = 0 and solve for x:

f(x) = 0

⇒ 1/6(x - 2)² - 6 = 0

⇒ 1/6(x - 2)² = 6

⇒ (x - 2)² = 36

⇒ x - 2 = ±6

⇒ x = 8, -4

Therefore, the other x-axis intercept is 8

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3 years ago

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3 years ago

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3 years ago

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Answer:

Step-by-step explanation:

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