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zzz [600]
2 years ago
14

Consider the quadratic function: y = 2x^2 + 7x + 10

Mathematics
1 answer:
arsen [322]2 years ago
7 0

Answer:

y-intercept: 10

concavity: function opens up

min/max: min

Step-by-step explanation:

1.) The definition of a y-intercept is what the resulting value of a function is when x is equal to 0.

Therefore, if the function's equation is given, to find y-intercept simply plug in 0 for the x-values:

y = 2x^2+7x+10 = 2(0)^2 + 7(0)+10 = 2(0) + 0 + 10 = 0 + 10 = 10

y intercept ( f(0) )= 10

2.) In order to find concavity (whether a function opens up or down) of a quadratic function, you can simply find the sign associated with the x^2 value. Since 2x^2 is positive, the concavity is positive. This is basically possible, since it is identifying any reflections affecting the y-values / horizontal reflections.

3.) In order to find whether a quadratic function has a maximum or minimum, you can use the concavity of the function. The idea is that if the function opens downwards, the vertex would be at the very top, resulting in a maximum. If a function was open upwards, the vertex would be at the very bottom, meaning there is a minimum. Like the concavity, if the value associated with x^2 is positive, there is a minimum. If it is negative, there is a maximum. Since 2x^2 is positive, the function has a minimum.

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Marissa's Fashions purchases designer boots from a manufacturer for $50.88 per pair. Marissa then adds a certain amount to the p
KATRIN_1 [288]

Answer:

Markup of _66.67_ % or $ _33,92_ per pair of boots

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That can be done simply with a cross-multiplication (106.25 represents total price with 6.25% tax, and 100 represent amount of sales before tax)

\frac{90.10}{106.25} = \frac{x}{100}

if we isolate x we have x = (90.10 * 100) / 106.25 = $84.80

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Now, let's calculate the markup percentage by see how much $33.92 represents compared to the initial price of $50.88:

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6 0
3 years ago
Find an equation of the tangent line to f(x) = 5x2 − 2x + 10 at x = 7.
laiz [17]

Answer:

y=68x-235

Step-by-step explanation:

f(x) = 5x^2-2x + 10

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\implies f'(x)=10x-2

Substitute x=7 into f'(x):

\implies f'(7)=10(7)-2=68

Therefore, 68 is the gradient of the tangent line at x=7:

\implies y-y_1=68(x-x_1)

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\implies y=68x-235

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Answer:

x + 11

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Step-by-step explanation:

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Angelina_Jolie [31]
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\\ \rm\Rrightarrow Perimeter=2(L+B)

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2 years ago
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