The quadratic has a vertex of (10,-9) and y-intercept of (0,-4). write an equation in vertex form. plz

Hello there!

Knowing that the vertex form of the quadratic equation is
y=a(x-h)^2+k where (h,k) represents the vertex, and the a value represents the leading coefficient of the quadratic equation in standard form, first plug in your known values (your given coordinate point can be plugged into the x and y values, and your given vertex can be plugged into h and k):
-4=a(0-10)^2-9

Because your a value is still unknown, you can use your given values in the equation to solve for a:
-4=a(-10)^2-9
-4=100a-9
100a=5
a=1/20

Now that you have your a value, you can plug it into your vertex form as well as your vertex values to get that your equation in vertex form is:
y=1/20(x-10)^2-9

Ac equals 35 cm long