Math Help: Solve Quadratic Function Intercepting X-Axis

  • Thread starter ohlhauc1
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In summary, the problem involves finding the equation of a quadratic function in transformational form using given intercepts and a point. To solve, you can plug in the coordinates to isolate the unknowns and then use this information to find the values of h and k. Once these values are known, you can rewrite the equation in terms of a, k, and h and plug in the final coordinate to find the equation. The use of quadratic regression or the quadratic formula is not allowed.
  • #1
ohlhauc1
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Hey! My friend asked me to help him solve this math problem, but I could only get so far to say the x-value is (1,0). Could you please show me how to do the problem? Thanks.

It is:

If a quadratci function intercepts the x-axis at (-2,0) and (4,0) and also goes through the point (7,74), what is its equation in transformational form?

YOU ARE NOT ALLOWED TO USE QUADRATIC REGRESSION OR THE QUADRATIC FORMULA!

The form for transformational form if you do not know is: a(y+k)=(x+h)^2
 
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  • #2
If I just plug the values in the coordinates we know in the transformational form, I can isolate all 3 unknowns. Or am I missing something?
 
  • #3
How would you do that? I do not think it is possible.
 
  • #4
1) ak = (-2+h)^2

2) ak = (4+h)^2

1 and 2 combined gives (-2+h)^2 = (4+h)^2, which allows you to find h.

Now that you know h, you can get summon back 1) or 2) to get an expression of k in terms of a. Rewrite a(y+k)=(x+h)^2 by writing k in terms of a and plug the last coordinate.
 

FAQ: Math Help: Solve Quadratic Function Intercepting X-Axis

What is a quadratic function?

A quadratic function is a mathematical function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the independent variable. It is a type of polynomial function that has a degree of 2.

What does it mean for a quadratic function to intercept the x-axis?

When a quadratic function intercepts the x-axis, it means that the graph of the function crosses or touches the x-axis at one or more points. These points are also known as the zeros or roots of the function.

How do you solve for the x-intercepts of a quadratic function?

To find the x-intercepts of a quadratic function, you can set the function equal to 0 and solve for x using the quadratic formula or by factoring. The resulting values of x are the x-intercepts of the function.

What does the x-intercept represent in a quadratic function?

The x-intercept of a quadratic function represents the points where the graph of the function crosses the x-axis. These points correspond to the values of x where the function has a y-value of 0.

Why is it important to find the x-intercepts of a quadratic function?

Finding the x-intercepts of a quadratic function is important because it allows us to identify the points where the function crosses the x-axis and find the roots of the function. This information can be used to analyze the behavior of the function and solve real-world problems.

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