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2 years ago

The vertex of this parabola is at (-5, -2). When the x-value is -4, the

Mathematics

1 answer:

Advocard [28]2 years ago

7 0

Answer:

The answer to your question is letter A

Step-by-step explanation:

Data

Vertex = (-5, -2)

Point = (-4, 2)

This is a vertical parabola the opens upwards.

The equation is

(x - h)² = 4p(y - k)

Substitution

(-4 + 5)² = 4p (2 + 2)

Simplification

1² = 4p(4)

1 = 16p

p = 1/16

Equation of the parabola

(x + 5)² = 4/16(y + 2)

x² + 10x + 25 = 1/4y + 1/2

Conclusion

The coefficient of the squared expression is 1

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2 years ago

Solve the quadratic equation by completing the square.x ^ 2 + 16x + 59 = 0First, choose the appropriate form and fill in the bla

nikitadnepr [17]

Given:

There are given the quadratic equation:

$x^2+16x+59=0$

Explanation:

To find the value of x by using completing the square, first, we need to subtract 59 on both sides of the given equation:

So,

From the given equation:

$\begin{gathered} x^2+16x+59=0 \\ x^2+16x+59-59=0-59 \\ x^2+16x=-59 \end{gathered}$

Now,

Take half of the x term and square it:

So,

From the x term,

$\lbrack16\cdot\frac{1}{2}\rbrack^2=64$

Then,

Add 64 on both sides of the above equation.

So,

$\begin{gathered} x^2+16x=-59 \\ x^2+16x+64=-59+64 \\ x^2+16x+64=5 \\ (x+8)^2=5 \end{gathered}$

Hence, an option first is correct:

$(x+8)^2=5$

Now,

From the above square:

$\begin{gathered} (x+8)^2=5 \\ x+8=\pm\sqrt[]{5} \end{gathered}$

Then,

Subtract 8 from both sides of the equation;;

So,

$\begin{gathered} x+8=\pm\sqrt[]{5} \\ x+8-8=\pm\sqrt[]{5}-8 \\ x=\pm\sqrt[]{5}-8 \\ x=\sqrt[]{5}-8,\pm\sqrt[]{5}-8 \\ x=-5.7639,-10.236067 \end{gathered}$

Final answer:

Hence, the value of x is shown below:

$x=(-5.76,-10.24)$

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1 year ago