Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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 :

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

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.