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Nikitich [7]
3 years ago
13

(5 pts) A quadratic function f is given by f(x) = ax2 + bx + c where a is not 0. Select all

Mathematics
1 answer:
Vsevolod [243]3 years ago
8 0

Answers:

  • a) True. Plug in x = 0 and it leads to y = c. Therefore, the point (0,c) is on the parabola.
  • b) False. Plug in y = 0 and apply the quadratic formula. One x intercept may sometimes be x = c, but it could easily be other values as well. Or perhaps you may not get any real number solutions at all. See part d) below.
  • c) True. If a < 0, then the leading coefficient is negative. Overall, both endpoints will tend toward negative infinity to produce a parabola that opens downward.
  • d) False. The quadratic may have one x intercept or it may not have any x intercepts at all. It depends on what the discriminant d = b^2 - 4ac is equal to. If d < 0, then we have no x intercepts. If d = 0, then we have exactly 1 x intercept. If d > 0, then we have two different x intercepts.
  • e) True. The vertex's x coordinate is -b/(2a). If b = 0, then the x coordinate of the vertex is 0. The vertical line x = 0 is directly on top of the y axis.
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First one

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y = -3x + 5

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x = (5 - y)/3

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Part ion even know of the hardest test
ladessa [460]

Given:

The equation of a line is:

y=-\dfrac{5}{7}x+2

A line passes through the point (-5,-3) and perpendicular to the given line.

To find:

The equation of the line.

Solution:

Slope intercept form of a line is:

y=mx+b                 ...(i)

Where, m is the slope and b is the y-intercept.

We have,

y=-\dfrac{5}{7}x+2          ...(ii)

On comparing (i) and (ii), we get

m=-\dfrac{5}{7}

We know that the product of slopes of two perpendicular lines is always -1.

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-\dfrac{5}{7}\times m_2=-1

m_2=\dfrac{7}{5}

Slope of the required line is \dfrac{7}{5} and it passes through the point (-5,-3). So, the equation of the line is:

y-y_1=m_2(x-x_1)

y-(-3)=\dfrac{7}{5}(x-(-5))

y+3=\dfrac{7}{5}(x+5)

Using distributive property, we get

y+3=\dfrac{7}{5}(x)+\dfrac{7}{5}(5)

y+3=\dfrac{7}{5}x+7

y=\dfrac{7}{5}x+7-3

y=\dfrac{7}{5}x+4

Therefore, the equation of the line is y=\dfrac{7}{5}x+4. Hence, option A is correct.

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Tanzania [10]

Answer:

x1= -1-√17/4

x2= -1+√17/4

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