Find the x-intercepts of the parabola with vertex (5,-4) and y-intercept (0,96). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth. ​

Accepted Solution

Answer:The x-intercepts are (x1,y1)=(4,0)(x2,y2)=(6,0)Step-by-step explanation:we know thatThe equation of the given parabola is [tex](y-k)=a(x-h)^{2}[/tex]we have the vertex is the point (5,-4)substitute[tex](y+4)=a(x-5)^{2}[/tex]The y-intercept is the point (0,96)substitute and solve for a[tex](96+4)=a(0-5)^{2}[/tex][tex]100=a(25)[/tex][tex]a=100/25=4[/tex]The equation of the vertical parabola is equal to[tex](y+4)=4(x-5)^{2}[/tex]Find the x-interceptsRemember thatThe x-intercepts are the values of x when the value of y is equal to zeroFor y=0[tex]4=4(x-5)^{2}[/tex]Simplify[tex]1=(x-5)^{2}[/tex]Rewrite[tex](x-5)^{2}=1[/tex]square root both sides[tex](x-5)=(+/-)1[/tex][tex]x=(+/-)1+5[/tex][tex]x=(+)1+5=6[/tex][tex]x=(-)1+5=4[/tex]thereforeThe x-intercepts are(x1,y1)=(4,0)(x2,y2)=(6,0)