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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Step-by-step answer

09.07.2023, solved by verified expert
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minimum, coordinates of vertex: (-3,-11)

explanation:

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

x coordinates on vertex:

solving steps:

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

Find y-coordinate on vertex:

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

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

coordinates: (-3,-11) thus minimum

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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:

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

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

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

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

As the leading term of the quadratic function (Determine the coordinates of the vertex for each, №18009965, 24.11.2022 00:34) is positive, the parabola will open upwards, so the vertex is its minimum point.

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Faq

Mathematics
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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