Use the image to answer the question.
A coordinate plane's x-axis ranges from negative 10 to 2 and its y-axis ranges from negative 4 to 4, both by 1-unit increments. A concave down parabola is drawn passing through the 2nd, 3rd, and 4th quadrants.
Which response is the correct way to write the equation in vertex form for the function?
Responses
y=−14(x+2)2+4
y is equal to negative 1 fourth times open paren x plus 2 close paren squared plus 4 - no response given
y=−14(x−2)2+4
y is equal to negative 1 fourth times open paren x minus 2 close paren squared plus 4 - incorrect
y=−14(x+4)2+2
y is equal to negative 1 fourth times open paren x plus 4 close paren squared plus 2 - not selected, this is the correct answer
y=−14(x−4)2+2
y=-1/4(x+4)^2 + 2
why is this the correct answer
The concave down parabola in the 2nd, 3rd, and 4th quadrants opens downwards and is shifted to the left of the origin. The vertex of the parabola is at (-4, 2).
In vertex form, a parabola's equation is of the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Since the vertex is at (-4, 2), we have h = -4 and k = 2.
Plugging these values into the equation gives us y = -1/4(x+4)^2 + 2. So, y=-1/4(x+4)^2 + 2 is the correct equation in vertex form for this function.