Value of b, y-intercept of Quadratic graph

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Discussion Overview

The discussion revolves around determining the value of b, the y-intercept of a quadratic graph represented by the equation y = x² + ax + b. Participants are analyzing the implications of the graph intersecting the x-axis at the points (2, 0) and (4, 0), exploring the relationships between the coefficients and the roots of the quadratic equation.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant seeks assistance in finding the value of b given the roots of the quadratic equation.
  • Another participant provides the factored form of the quadratic equation, y = (x - 2)(x - 4), and expands it to y = x² - 6x + 8.
  • Multiple participants derive equations based on the roots: 2a + b = -4 and 4a + b = -16, suggesting a method to solve for a and b.
  • One participant expresses gratitude for the clarification provided by others, indicating that the discussion helped them understand the problem better.

Areas of Agreement / Disagreement

Participants generally agree on the method to derive the equations from the given roots, but there is no consensus on the final values of a and b, as the discussion does not resolve these equations.

Contextual Notes

The discussion does not address potential assumptions regarding the values of a and b, nor does it resolve the mathematical steps necessary to find these values from the derived equations.

gazparkin
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Hi,

Can anyone help me understand how I get to the answer on this one?

The diagram shows a sketch of the graph of y = x2 + ax + b

The graph crosses the x-axis at (2, 0) and (4, 0).

Work out the value of b.Thank you in advance!
 

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Mathematics news on Phys.org
$$y=(x - 2)(x - 4)=x^2-6x+8$$
 
The graph is of y= x^2+ ax+ b and we are told that the graph goes through (2, 0). That means that when x= 2, y= 0. So we must have 0= 2^2+ a(2)+ b= 4+ 2a+ b or 2a+ b= -4. We are also told that the graph goes through (4, 0). That means that when x= 4, y= 0. So we must have 0= 4^2+ a(4)+ b= 16+ 4a+ b or 4a+ b= -16.

Solve the two equations, 2a+ b= -4 and 4a+ b= -16, for a and b.
 
HallsofIvy said:
The graph is of y= x^2+ ax+ b and we are told that the graph goes through (2, 0). That means that when x= 2, y= 0. So we must have 0= 2^2+ a(2)+ b= 4+ 2a+ b or 2a+ b= -4. We are also told that the graph goes through (4, 0). That means that when x= 4, y= 0. So we must have 0= 4^2+ a(4)+ b= 16+ 4a+ b or 4a+ b= -16.

Solve the two equations, 2a+ b= -4 and 4a+ b= -16, for a and b.

Thank you for this - really helped me understand.
 

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