Question #576da
2 Answers
Explanation:
#"to find the x-intercepts solve "x^2+10x+24=0#
#"the factors of 24 which sum to + 10 are + 4 and + 6"#
#rArr(x+6)(x+4)=0#
#"equate each factor to zero and solve for x"#
#x+6=0rArrx=-6larrcolor(red)" x-intercept"#
#3x+4=0rArrx=-4larrcolor(red)" x-intercept"#
#"given the parabola in standard form "ax^2+bx+c#
#"the x-coordinate of the vertex/ axis of symmetry is"#
#x_(color(red)"vertex")=-b/(2a)#
#y=x^2+10x+24" is in standard form"#
#"with "a=1,b=10,c=24#
#x_(color(red)"vertex")=-10/2=-5#
#"substitute this value into the equation for y"#
#rArry_(color(red)"vertex")=(-5)^2+10(-5)+24=-1#
#rArrcolor(magenta)"vertex "=(-5,-1)#
#"axis of symmetry is "x=-5#
graph{(y-x^2-10x-24)(y-1000x-5000)=0 [-10, 10, -5, 5]}
The x intercepts are
The axis of symmetry is:
The vertex is
Explanation:
In order to find the x intercepts, we will substitute
We will use the short quadratic formula
Then
and the x intercepts are
The axis of symmetry is:
We simply will get the second coordinate of the vertex by substituting x=-5 in the given F(x):
Then
graph{x^2+10x+24 [-10, 5, -5, 5]}