Answer: P(1) = (1+10)(1+3) = 11 * 4 = 44
Step-by-step explanation: The expression P(x)=(x+10)(x+3) defines a quadratic function, also known as a parabola. The graph of a quadratic function is a U-shaped curve. The vertex of the parabola is the point where the function reaches its maximum or minimum value.
To find the vertex of the parabola, we can use the following steps:
Find the x-coordinate of the vertex: x = -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively.
Find the y-coordinate of the vertex by evaluating the function at the x-coordinate of the vertex.
In the case of P(x)=(x+10)(x+3), a=1 and b=13. Therefore, the x-coordinate of the vertex is:
x = -b/2a = -13/(2*1) = -13/2
To find the y-coordinate of the vertex, we evaluate P(x) at x=-13/2:
P(-13/2) = (-13/2+10)(-13/2+3) = 1/2 * -1/2 = -1/4
Therefore, the vertex of the parabola is at the point (-13/2,-1/4).
To find P(x) at a given value of x, we simply substitute that value of x into the expression and evaluate. For example, to find P(1), we would substitute x=1 into the expression and evaluate:
P(1) = (1+10)(1+3) = 11 * 4 = 44
Therefore, P(1)=44.
In conclusion, the expression P(x)=(x+10)(x+3) defines a quadratic function with vertex at the point (-13/2,-1/4). To find P(x) at a given value of x, we simply substitute that value of x into the expression and evaluate.