Mathematics : asked on bihanna1234

24.11.2022

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

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09.07.2023, solved by verified expert

Bibin (Bibi) P B

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

explanation:

x coordinates on vertex:

solving steps:

Determine the coordinates of the vertex for each, №18009965, 24.11.2022 00:34

Determine the coordinates of the vertex for each, №18009965, 24.11.2022 00:34

Determine the coordinates of the vertex for each, №18009965, 24.11.2022 00:34

Find y-coordinate on vertex:

coordinates: (-3,-11) thus minimum

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Bibin (Bibi) P B

Biology, Geography, Q&A Expert

21 791 answers

Unlock the full 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:

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

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

As the leading term of the quadratic function () is positive, the parabola will open upwards, so the vertex is its minimum point.

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Mathematics

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

Step-by-step answer

P Answered by Specialist

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

explanation:

$\sf y =x^2 +6x-2$

x coordinates on vertex:

solving steps:

$\sf \dfrac{-b}{2a}$ $\sf \dfrac{-6}{2(1)}$ $\sf -3$

Find y-coordinate on vertex:

$\sf y =x^2 +6x-2$

$\sf y =(-3)^2 +6(-3)-2$

$\sf y =-11$

$\mathrm{If}\:a < 0,\:\mathrm{then\:the\:vertex\:is\:a\:maximum\:value}$

$\mathrm{If}\:a 0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}$

coordinates: (-3,-11) thus minimum

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