A Step-by-Step Guide to Finding x-Intercepts of a Quadratic Equation

How to find the x-intercepts for the equation f(x)=a(x-h)^2+k

To find the x-intercepts of the equation f(x) = a(x-h)^2 + k, we need to set f(x) equal to zero and solve for x

To find the x-intercepts of the equation f(x) = a(x-h)^2 + k, we need to set f(x) equal to zero and solve for x. The x-intercepts are the points where the graph of the equation intersects the x-axis.

1. Start by setting f(x) equal to zero:
0 = a(x – h)^2 + k

2. Subtract k from both sides of the equation to isolate the quadratic term:
-k = a(x – h)^2

3. Divide both sides by a to further isolate the quadratic term:
-k/a = (x – h)^2

4. Take the square root of both sides to solve for x – h:
±√(-k/a) = x – h

Note: Since we are taking the square root, we need to consider both the positive and negative roots to find all possible x-intercepts.

5. Add h to both sides of the equation to solve for x:
x = h ± √(-k/a)

These are the x-values of the x-intercepts of the equation.

Now, let’s clarify the definitions of some terms:

– x-intercepts: The x-intercepts, also known as the roots or zeros of a function, are the points where the graph of the function intersects the x-axis. In other words, these are the values of x for which the y-coordinate (or function value) is equal to zero.

– f(x): f(x) represents the function, which is a mathematical rule that relates an input value x to an output value. In this case, the function is given as f(x) = a(x-h)^2 + k, where a, h, and k are constants.

– a: a is a constant that determines the shape of the quadratic curve. If a is positive, the curve opens upwards, and if a is negative, the curve opens downwards. The larger the absolute value of a, the narrow the curve becomes.

– h: h is a constant that represents the horizontal shift of the quadratic curve. It determines the x-coordinate of the vertex, which is the highest or lowest point on the curve.

– k: k is a constant that represents the vertical shift of the quadratic curve. It determines the y-coordinate of the vertex and moves the entire curve up or down without changing its shape.

By understanding these definitions and following the steps provided, you should be able to find the x-intercepts of the given quadratic equation.

More Answers: