How do you find the turning point of a quadratic equation? (The Formula)
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To find the turning point of a quadratic equation, you can use the formula:
1. Start with a quadratic equation in the form of y = ax^2 + bx + c, where a, b, and c are constants.
2. Calculate the x-coordinate of the turning point using the formula x = -b / (2a). This is also known as the line of symmetry for the quadratic equation.
3. Substitute the value of x into the equation to find the corresponding y-coordinate of the turning point.
So, the turning point of a quadratic equation is given by the coordinates (x, y), where x = -b / (2a) and y = ax^2 + bx + c.
To find the turning point of a quadratic equation, you can use the formula:
Turning point: (h, k)
h = -b/2a
k = f(h)
Where:
- The quadratic equation is in the form of ax^2 + bx + c = 0.
- (h, k) represents the coordinates of the turning point.
- a, b, and c are the coefficients of the quadratic equation:
- a: The coefficient of the squared term (x^2).
- b: The coefficient of the linear term (x).
- c: The constant term.
Let's go through the steps to find the turning point:
Step 1: Identify the values of a, b, and c from the quadratic equation.
Step 2: Use the formula for h to find the x-coordinate of the turning point:
h = -b/2a
Step 3: Substitute the value of h into the original equation to find the y-coordinate (the corresponding value of x):
k = f(h)
Step 4: The turning point coordinates are (h, k).
Keep in mind that if a is positive, the parabola opens upward, and the turning point is a minimum. If a is negative, the parabola opens downward, and the turning point is a maximum.