Identify the vertex first. Then use it to find the axis of symmetry.
Vertex Form: y=3(x+6)^2-83 Vertex: (-6,-83) Axis of Symmetry: x=-6 Opening: Opens up Graph:
Practice makes perfect
In order to graph the function we will rewrite the function into vertex form; identify a, h, and k; plot the vertex and points; and then put it together.
Rewriting Function
We have a quadratic function written in standard form, and we want to rewrite it in vertex form.
Standard Form:& y= ax^2+ bx+c
Given Equation:& y= 3x^2+ 36x+25
In the given equation, a= 3, b= 36, and c=25.
Let's now recall the vertex form of a quadratic function.
Vertex Form: y=a(x-h)^2+kIn this equation, a is the leading coefficient of the quadratic function, and the point (h,k) is the vertex of the parabola. By substituting our given values for a and b into the expression - b2a, we can find h.
Therefore, the (h,k) coordinate pair of the vertex is ( -6,-83). Moreover, since we already know that a= 3, we can rewrite the given function in vertex form.
y= 3 (x-( -6))^2+(-83) ↔ y= 3 (x+ 6)^2-83
Identify a, h, and k
We will first identify the constants a, h, and k. Recall that if a<0, the parabola will open downwards. Conversely, if a>0, the parabola will open upwards.
Vertex Form:& f(x)= a(x- h)^2+k
Function:& f(x)= 3 (x+ 6)^2-83
We can see that a= 3, h= -6, and k=-83. Since a is greater less than 0, the parabola will open upwards.
Plotting the Vertex and Points
Let's now plot the vertex ( h,k) and draw the axis of symmetry x= h. Since we already know the values of h and k, we know that the vertex is ( -6,-83). Therefore, the axis of symmetry is the vertical line x= -6.
We will now plot a point on the curve by choosing an x-value and calculating its corresponding y-value. Let's try x=-2.
