, 15.07.2019 19:00 MegRasmussen31

# Which of the following equations is of a parabola with a vertex at (0, -5)? y = (x - 5)2 y = (x + 5)2 y = x2 - 5 y = x2 + 5

Put 0 for x in each possible choice and see which one gives you y = -5.

The appropriate choice is
y = x² - 5

Of course, you know the vertex form is
y = a(x -h)² + k
for vertex (h, k) and scale factor "a".
Then for (h, k) = (0, -5), this is
y = ax² -5
Only one choice matches that: y = x² -5. (for a=1)
The equation

will have a parabola with a vertex at (0,-5) as the y intercept is - 5. Remember, quadratic equations can often be written in the form

Where a is the coefficient of the quadratic, b is the coefficient of the multiple and C is the vertex/y-intercept.

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Step-by-step explanation:

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Equation of parabola is y = x² - 5 .

Step-by-step explanation:

Given  : parabola with a vertex at (0, -5).

To find :  which of the following equations is of a parabola.

Solution : We have given  vertex at (0, -5).

Vertex form of parabola   y = a(x - h)² + k .

Where (h ,k ) is vertex

We have h = 0 , k = -5 .

Equation : y = 1(x - 0)² - 5

y = x² - 5 .

Therefore, Equation of parabola is y = x² - 5 .

The equation that has a vertex in (0, -5) is the first one.

Step-by-step explanation:

A standard form second degree equation is given by the following expression:

For which the vertex coordinates can be calculated by:

While "y" for the vertex can be found by applying this coordinate on the expression. Using this knowledge in each equation gives us:

1.

Therefore the vertex coordinate is:

This parabola has a vertex in (0,-5).

2.

Therefore the vertex coordinate is:

This parabola has a vertex in (0,5).

3.

Therefore the vertex coordinate is:

This parabola has a vertex in (-5,0).

4.

Therefore the vertex coordinate is:

This parabola has a vertex in (5,0).

The x, which is zero in this case will always be the number that goes on the inside of the equation, so far you have y=(x+0)^2 or y=x^2.

The y, which is negative will go on the end of the equation. So you get y=x^2-5

The equation is y=x^2-5 or C if it is multiple choice

The equation of a parabola with Vertex V=(h,k) is
y=a(x-h)^2+k
If the Vertex is V=(0,-5)=(h,k)→h=0, k=-5
Replacing h=0 and k=-5 in the equation above:
y=a(x-0)^2+(-5)
y=ax^2-5

Third option: y=x^2-5

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