We want to write the equation of the given parabola. To do so, let's recall the vertex form of a quadratic function.
y= a(x- h)^2+k
In this expression, a, h, and k are either positive or negative constants. Let's start by identifying the vertex.
The vertex of this parabola has coordinates ( 2,-9). This means that we have h= 2 and k=-9. We can use these values to partially write our function.
y= a(x-( 2))^2+(-9)
⇕
y= a(x-2)^2-9
We can see in the graph that the parabola opens upwards. Therefore, a will be a positive number. To find its value, we will use the given point that is not the vertex.
We can see above that the point has coordinates (0,- 5). Since this point is on the curve, it satisfies its equation. Hence, to find the value of a, we can substitute 0 for x and - 5 for y and simplify.
We found that a= 1. Now we can complete the equation of the curve.
y= 1(x-2)^2-9
To obtain the standard form of the quadratic function, we simplify the right-hand side of the equation.
