Write an equation for the quadratic function using the given information.
X=15, X=5
a point on the graph: (0,75)
If you mean the x-intercepts are at 5 and 15, then
y = a(x-5)(x-15)
75 = a(-5)(-15)
a = 1
so,
y = (x-5)(x-15)
x squared x^2-20x+75
To find the equation for a quadratic function, we need to use the information given - the x-intercepts (x=15 and x=5) and a point on the graph (0,75).
Step 1: Use the x-intercepts to find the "zeros" of the equation. Zeros are the values of x where the equation equals zero. Therefore, the zeros in this case are 15 and 5.
Step 2: Since the zeros are given, we can write the equation in factored form. The factored form of a quadratic equation is given as follows: (x - zero1)(x - zero2) = 0. Plugging in the values, we have (x - 15)(x - 5) = 0.
Step 3: Expand the equation obtained from step 2. Multiplying the two factors, we get x^2 - 20x + 75 = 0.
Step 4: Use the additional information given - a point on the graph (0,75) - to determine the value of "a" in the quadratic equation. The equation can be written as ax^2 + bx + c = 0, where a, b, and c are coefficients. Since the point (0,75) lies on the graph, we have 75 = a(0)^2 + b(0) + c. Simplifying this, we get 75 = c.
Step 5: Substitute the value of c into the expanded equation from step 3. Therefore, the final equation for the quadratic function is x^2 - 20x + 75 = 0.