Answer
vertex: (-5,0)
X-Intercept: (-5,0)
Y-Intercept: (0,25)
Work Step by Step
Formula: X^2+10x+25
To find the vertex, you must first find your A, B, and C values. For this equation, A= 1, B= 10, and C=25.
To get the x value of your vertex, let x= -B/2A. so..
x= -(10)/2(1)
x= -10/2
x= -5
Given the x value we just found, plug it into the x values of the original equation.
(-5)^2+10(-5)+25= f(-5)
25-50+25=f(-5)
-25+25=f(-5)
0=f(-5)
So, the vertex is (-5,0)
To find the x intercepts, set the y value to 0.
0=x^2+10x+25
To factor out this formula, you must find two values that add together to give you the B value, and that multiply together to give you the C value.
For this equation, (x+5)(x+5)=0.
x+5=0
subtract 5 from both sides, and x=-5
So the x intercept is (-5,0)
To find the y intercept, set the x values of the equation to 0.
f(x)= 0^2+10(0)+25
f(x)= 0+0+25
f(x)= 25
So the y-intercept is (0,25)
Since we are given 3 points on the graph, we are able to graph the equation, but to have a smaller graph, I'm going to find two more points using -6 and -4 as the x values.
so. f(-6)= (-6)^2+10(-6)+25
f(-6)= 36-60+25
f(-6)= -24+25
f(-6)= 1
So a point would be (-6,1)
f(-4)= (-4)^2+10(-4)+25
f(-4)= 16-40+25
f(-4)= -24+25
f(-4)= 1
The other point would be (-4,1)
The graph opens upward because the A value of the equation is greater than 0.
