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Dentify on which quadratic function is positive.

Olin [163]

Answer:

$\textsf{$y = 2x^2 - 17x + 30$: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}$

$\textsf{$y = - x^2 - 6x - 8$: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}$

Step-by-step explanation:

A function is positive when it is above the x-axis, and negative when it is below the x-axis.

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Given quadratic equation:

$y = 2x^2 - 17x + 30$

Factor the equation:

$\implies y = 2x^2 - 17x + 30$

$\implies y = 2x^2 - 5x-12x + 30$

$\implies y=x(2x-5)-6(2x-5)$

$\implies y=(x-6)(2x-5)$

The x-intercepts of the parabola are when y = 0.

To find the x-intercepts, set each factor equal to zero and solve for x:

$\implies x-6=0 \implies x=6$

$\implies 2x-5=0 \implies x=\dfrac{5}{2}$

Therefore, the x-intercepts are x = ⁵/₂ and x = 6.

The leading coefficient of the given function is positive, so the parabola opens upwards.

The function is positive when it is above the x-axis.

Therefore, the function is positive for the values of x less than the smallest x-intercept and more than the largest x-intercept:

$\textsf{Solution: \quad $x < \dfrac{5}{2}$ \;and \;$x > 6$}$

$\textsf{Interval notation: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}$

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Given quadratic equation:

$y = - x^2 - 6x - 8$

Factor the equation:

$\implies y = - x^2 - 6x - 8$

$\implies y = -(x^2 +6x +8)$

$\implies y = -(x^2 +4x +2x+8)$

$\implies y = -((x(x+4)+2(x+4))$

$\implies y = -(x+4)(x+2)$

The x-intercepts of the parabola are when y = 0.

To find the x-intercepts, set each factor equal to zero and solve for x:

$\implies x+4=0 \implies x=-4$

$\implies x+2=0 \implies x=-2$

Therefore, the x-intercepts are x = -4 and x = -2.

The leading coefficient of the given function is negative, so the parabola opens downwards.

The function is negative when it is below the x-axis.

Therefore, the function is negative for the values of x less than the smallest x-intercept and more than the largest x-intercept:

$\textsf{Solution: \quad $x < -4$ \;and \;$x > -2$}$

$\textsf{Interval notation: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}$

4 0

4 months ago

Read 2 more answers

The difference between a number and seven at least 12

lara [203]

Answer:

x=10.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

10. For f(x) = 3 - 5x, find f(-5). A. –22 B. -7 C. 3 D. 28

Artist 52 [7]

Answer:

D

Step-by-step explanation:

$3 - 5( - 5) \\ 3 - ( - 25) \\ 3 + 25 \\ 28$

4 0

2 years ago

This question is confusing to me please help..

lisabon 2012 [21]

Answer:

5

Step-by-step explanation:

First off find how many bowls and vases combined

12 bowls and 8 vases therefore 20

to find 1/4 of a number divide by 4

therefore, 20/4 is 5

5 0

2 years ago

Find the x and y intercepts of the graph of the linear equation 3x+6y=24

steposvetlana [31]

Answer:

x =(0,6) y=(0,8)

Step-by-step explanation:

3x+6y=24

make x =0

3(0)+6y=24

6y=24

y=6 x=0

8 0

2 years ago