Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
The vertex form of the parabola is
[tex]y=a(x-h)^2+k[/tex]Where (h, k) are the coordinates of its vertex
Since the vertex of the parabola is (5, -3), then
h = 5 and k = -3
Substitute them in the form above
[tex]\begin{gathered} y=a(x-5)^2+(-3) \\ y=a(x-5)^2-3 \end{gathered}[/tex]To find the value of (a) we will use the given point (1, 5)
Substitute x by 1 and y by 5
[tex]\begin{gathered} 5=a(1-5)^2-3 \\ 5=a(-4)^2-3 \\ 5=16a-3 \end{gathered}[/tex]Add both sides by 3
[tex]\begin{gathered} 5+3=16a-3+3 \\ 8=16a \end{gathered}[/tex]Divide both sides by 16 to find (a)
[tex]\begin{gathered} \frac{8}{16}=\frac{16a}{16} \\ \frac{1}{2}=a \\ a=\frac{1}{2} \end{gathered}[/tex]Substitute a by 1/2 in the equation above, then
a. The equation of the parabola is
[tex]y=\frac{1}{2}(x-5)^2-3[/tex]Let us substitute x and y in the equation by each answer
Since x = 0 and y = 3
[tex]\begin{gathered} 3=\frac{1}{2}(0-5)^2-3 \\ 3=12.5-3 \\ 3=9.5 \\ \text{LHS}\ne RHS \end{gathered}[/tex]Since x = -1 and y = 9
[tex]\begin{gathered} 9=\frac{1}{2}(-1-5)^2-3 \\ 9=\frac{1}{2}(-6)^2-3 \\ 9=\frac{1}{3}(36)-3 \\ 9=12-3 \\ 9=9 \\ \text{LHS}=\text{RHS} \end{gathered}[/tex]The point (-1, 9) lies on the parabola
The answer is b
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
