Find the x-intercepts of the parabola withvertex (6,-5) and y-intercept (0,175).Write your answer in this form: (x1,71),(x2,42).If necessary, round to the nearest hundredth.Enter the correct answer.

Answer:The x-intercepts are (5,0) and (7,0)Step-by-step explanation:we know thatThe equation of a vertical parabola in vertex form is equal to[tex]y=a(x-h)^{2}+k[/tex]wherea is a coefficient(h,k) is the vertexIn this problem we have(h,k)=(6,-5)substitute[tex]y=a(x-6)^{2}-5[/tex]Find the coefficient awith the y-intercept (0,175) substitute the value of x and the value of y in the equationFor x=0, y=175[tex]175=a(0-6)^{2}-5[/tex][tex]175=36a-5[/tex][tex]36a=180[/tex][tex]a=5[/tex]substitute[tex]y=5(x-6)^{2}-5[/tex]Find the x-interceptsRemember that the x-intercepts are the values of x when the value of y is equal to zeroFor y=0[tex]0=5(x-6)^{2}-5[/tex][tex]5(x-6)^{2}=5[/tex]simplify[tex](x-6)^{2}=1[/tex]square root both sides[tex]x-6=(+/-)1[/tex][tex]x=6(+/-)1[/tex][tex]x=6(+)1=7[/tex][tex]x=6(-)1=5[/tex]thereforeThe x-intercepts are (5,0) and (7,0)