Mathematics, 09.03.2022 15:40 etxchrissy

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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Answer from: bankscorneliuso39

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

Answer from: keonburkes9

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:

$\dfrac{dy}{dx}=2x+6$

$\dfrac{dy}{dx}=0\implies 2x+6=0 \implies x=-3$

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

$\implies (-3)^2+6(-3)-2=-11$

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

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

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

Answer from: Quest

h= 12 inches

step-by-step explanation:

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