Question

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Answer 1

Answer:

=> the passing point's y cord is lower than vertex, meaning it is a reflection
$y=-a\left(x+h\right)^{2}-k$

=>Apply the vertex to hk form
$y=-a\left(x+4\right)^{2}-1$
=> Find a by plugging X and Y of the passing through point

$-3=-a\left(-2+4\right)^2-1$

=> solve
$-4a-1+1=-3+1$

$a=\frac{1}{2}$

Therefore the equation for this is,

$y=-\frac{1}{2}\left(x+4\right)^{2}-1$

Answer 2

Answer:

$y=-\dfrac{1}{2}(x+4)^2-1$

Step-by-step explanation:

Vertex form:  $y=a(x-h)^2+k$  

where:

• $(h, k)$ is the vertex
• $a$ is some constant

Given:

• vertex = (-4, -1)
• point on parabola = (-2, -3)

Substitute given values into the formula to find $a$:

$\implies -3=a((-2)-(-4))^2+(-1)$

$\implies -3=a(2)^2-1$

$\implies -3=4a-1$

$\implies -2=4a$

$\implies a=-\dfrac{2}{4}=-\dfrac{1}{2}$

Therefore, the equation of the parabola is:

$y=-\dfrac{1}{2}(x+4)^2-1$