Jlynnbaileyjbidn
Answered

IDNLearn.com is your go-to platform for finding accurate and reliable answers. Our experts are ready to provide prompt and detailed answers to any questions you may have.

Determine the coordinates of the vertex for each quadratic function and whether the parabola has a maximum or minimum. 4. y = x² +6x-2​

Sagot :

Fieryanswererftidn

Answer:

minimum, coordinates of vertex: (-3,-11)

explanation:

[tex]\sf y =x^2 +6x-2[/tex]

x coordinates on vertex:

solving steps:

  • [tex]\sf \dfrac{-b}{2a}[/tex]
  • [tex]\sf \dfrac{-6}{2(1)}[/tex]
  • [tex]\sf -3[/tex]

Find y-coordinate on vertex:

[tex]\sf y =x^2 +6x-2[/tex]

[tex]\sf y =(-3)^2 +6(-3)-2[/tex]

[tex]\sf y =-11[/tex]

[tex]\mathrm{If}\:a < 0,\:\mathrm{then\:the\:vertex\:is\:a\:maximum\:value}[/tex]

[tex]\mathrm{If}\:a > 0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}[/tex]

coordinates: (-3,-11) thus minimum

Semsee45idn

Answer:

vertex = (-3, -11)

minimum

Step-by-step explanation:

The vertex of a parabola is its turning point (stationary point).

Therefore, the x-coordinate of the vertex can be determined by differentiating the function, setting it zero and solving for x:

[tex]\dfrac{dy}{dx}=2x+6[/tex]

[tex]\dfrac{dy}{dx}=0\implies 2x+6=0 \implies x=-3[/tex]

Substitute found value for x into the original function to find the y-coordinate:

[tex]\implies (-3)^2+6(-3)-2=-11[/tex]

Therefore, the vertex is (-3, -11)

As the leading term of the quadratic function ([tex]x^2[/tex]) is positive, the parabola will open upwards, so the vertex is its minimum point.

We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.