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mel-nik [20]
3 years ago
11

Vertex= Y-intercept= X-intercept= Range= Axis of symmetry =

Mathematics
1 answer:
AURORKA [14]3 years ago
6 0

Answer:

Vertex = (1 , 4)

Y-intercept = (0 , 3)

X-intercept = (-1 , 0) and (3 , 0)

Range is y ≤ 4

Axis of symmetry is at x = 1

Step-by-step explanation:

The quadratic function y = ax² + bx + c is represented graphically by a parabola

  • The parabola has a vertex point (h , k) which is minimum point if the parabola is opened upward or maximum if it is oped downward
  • The axis of symmetry of the parabola is a vertical line passes through the vertex point and its equation is x = h
  • The y-intercept is the intersection point between the parabola and the y-xis (value of y at x = 0)
  • The x-intercepts are the point of intersection between the parabola and the x-axis (values of x at y = 0)
  • The range of the quadratic function is y ≥ k, if the parabola is opened upward or y ≤ k if the parabola is opened downward

From the attached graph

∵ The parabola is opened downward

∵ Its highest point is (1 , 4)

∴ h = 1 and k = 4

∴ Its vertex = (1 , 4)

∵ The parabola intersects the y-axis at point (0 , 3)

∴ The y-intercept = (0 , 3)

∵ The parabola intersects the x-axis at points (-1 , 0) and (3 , 0)

∴ The x-intercept = (-1 , 0) and (3 , 0)

∵ The parabola is opened downward

∴ The range is y ≤ k

∵ k is the value of y of the vertex point

∴ k = 4

∴ The range is y ≤ 4

The axis of symmetry of the parabola is a vertical line passes through the vertex point

∵ The equation of the axis of symmetry is x = h

∵ h is the x-coordinate of the vertex point

∴ h = 1

∴ The axis of symmetry is at x = 1

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------------------------------------------------------------<span>
Ratio 
------------------------</span>---------------------------------<span>--
BC:AC:AB
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</span>-----------------------------------------------------------
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</span>-----------------------------------------------------------<span>
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</span>-----------------------------------------------------------
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</span>-----------------------------------------------------------
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</span>-----------------------------------------------------------<span>
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</span>------------------------------------------------------------
Length
-----------------------------------------------------------
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---------------------------------</span>---------------------------------<span>
Perimeter
</span>------------------------------------------------------------------
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</span>------------------------------------------------------------------
<span>Answer: The perimeter is 36cm
</span>------------------------------------------------------------------<span>

</span>------------------------------------------------------------------
<span>Area
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</span>------------------------------------------------------------------
Answer: Area = 54cm²
------------------------------------------------------------------<span>

Given that the biggest ratio is AB
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AB = 15 cm

------------------------------------------------------------------
Answer: Hypotenuse = AB = 15cm
------------------------------------------------------------------
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