Mathematics, 03.02.2020 13:01 beausisugpula

Find the x intercepts of the parabola with vertex (-1,-16) and y intercept (0,-15)

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Answer from: Shelbs01

first, write the equation of the parabola in the required form:
(y - k) = a·(x - h)²

Here, (h, k) is given as (-1, -16).
So you have:
(y + 16) = a · (x + 1)²

Unfortunately, a is not given. However, you do know one additional point on the parabola: (0, -15):

-15 + 16 = a· (0 + 1)²
.·. a = 1

.·. the equation of the parabola in vertex form is
y + 16 = (x + 1)²

The x-intercepts are the values of x that make y = 0. So, let y = 0:

0 + 16 = (x + 1)²
16 = (x + 1)²

We are trying to solve for x, so take the square root of both sides - but be CAREFUL!

± 4 = x + 1 remember both the positive and negative roots of 16

Solving for x:
x = -1 + 4, x = -1 - 4
x = 3, x = -5.

Or, if you prefer, (3, 0), (-5, 0).

Answer from: Quest

step-by-step explanation:

f(x)=2x^2 -1

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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Find the x intercepts of the parabola with vertex (-1,-16) and y intercept (0,-15)...

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