SOLUTION: 1. Find an equation for a quadratic function whose only x-intercept is (5,0). 2. Find the x-coordinate of the vertex of a parabola that contains the points (-2,7) and (9,7).

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1. Find an equation for a quadratic function whose only x-intercept is (5,0). 2. Find the x-coordinate of the vertex of a parabola that contains the points (-2,7) and (9,7).       Log On


   

Question 629272: 1. Find an equation for a quadratic function whose only x-intercept is (5,0).
2. Find the x-coordinate of the vertex of a parabola that contains the points (-2,7) and (9,7). Can you find the coordinates of the vertex?
3. Find an equation for a quadratic function that has vertex (4,3) and opens up. How many x-intercepts will the graph of the function have?
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
1. y+=+%28x-5%29%5E2 or y+=+x%5E2+-+10x+%2B+25
2. Since the y-coordinates of (-2,7) and (9,7) are the same.
The x-coordinate of the vertex is equal to the average of x-coordinates of
(-2,7) and (9,7).
x-coordinate of vertex = %28-2%2B9%29%2F2+=+highlight%287%2F2%29
We can only find the x-coordinate of the vertex but not the y-coordinate because we need another point to find the y-coordinate.
3. The quadratic equation is y+=+a%28x-4%29%5E2+%2B+3, where a%3C%3E0.
There are no x-intercepts because the lowest point (4,3) is above the x-axis.