Can someone help please?

Mathematics

1 answer:

Vlada [557]2 years ago

5 0

Answer:

Step-by-step explanation:

Vertex of the given parabola = (1, -4)

Since, vertex form of a parabola is given by,

y = (x - h)² + k

Here (h, k) is the vertex

Now substitute the coordinates (1, -4) in the equation.

y = (x - 1)²- 4 [Vertex Form]

Further solve this equation,

y = x² - 2x + 1 - 4

y = x² - 2x - 3 [Standard form]

Further write this equation in the factored form,

y = x² - 3x + x - 3

y = x(x - 3) + 1(x - 3)

y = (x + 1)(x - 3) [Factored form]

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Through (-4,5) and parallel to y = -3/2x-5

Ratling [72]

**Disclaimer** Hi there! I assumed the question to be asking for a line expression. The following answer will be according to this understanding. Please let me know if I am incorrect and I will modify my answer correspondingly

Answer: $\Large\boxed{y-5=-\dfrac{3}{2} (x+4)}$

Step-by-step explanation:

Given information

$\text{Pass~through~point}=(x_1,~y_1)=(-4,~5)$

$\text{Parallel~to}:y=-\dfrac{3}{2} x-5$

Given equation form

Point-slope form is the most efficient way to write the expression

$\text{Point-slope form}:y-y_1=m(x-x_1)$

$(x_1,~y_1)=\text{A point that the line passes through}$

$m=\text{Slope}$

Determine the slope

$\text{Since the line is parallel to } y=-\dfrac{3}{2} x-5 \text{ , by the property of parallel}\\\text{lines, the slope of the given line is also }-\dfrac{3}{2}$