How do you find the vertex and axis of symmetry for #y = 4x^2 + 7#?

Question

Isaiah Anthony · Accepted Answer

The vertex is at #(x,y) = (0,7)#
The axis of symmetry is #x=0# #color(white)("XXXX")##y = m(x-a)^2+b# #color(white)("XXXXXXXX")#, where the vertex is at #(a,b)#, is the general vertex form for a quadratic. It is simple to convert #y=4x^2+7# into vertex form as follows: #color(white)("XXXX")##y = 4(x-0)^2+7# #color(white)("XXXXXXXX")#, where the vertex is at #(0,7)#. Because the equation is that of a parabola in standard position (opening upward), the vertical line passing through the vertex, or #x=0#, is the axis of symmetry.

HIX Tutor · Answer

undefined To find the vertex and axis of symmetry for the equation y = 4x^2 + 7, you can follow these steps:

Step 1: Write down the equation: y = 4x^2 + 7.

Step 2: Identify the values of "a," "b," and "c" in the form of y = ax^2 + bx + c. In this case, "a" is 4, "b" is 0, and "c" is 7.

Step 3: The x-coordinate of the vertex can be found using the formula: x = -b / (2a). Substitute the values: x = -0 / (2*4). Simplify: x = 0 / 8, which is equal to 0.

Step 4: Substitute the value of x found in step 3 into the equation to find the y-coordinate of the vertex. y = 4(0)^2 + 7. Simplify: y = 0 + 7, which is equal to 7.

Therefore, the vertex is (0, 7).

Step 5: The axis of symmetry is a vertical line that passes through the vertex. In this case, the equation of the axis of symmetry is x = 0.

So, the vertex is (0, 7) and the axis of symmetry is x = 0.

Ethan Adkins · Answer

undefined To find the vertex of the quadratic function y = 4x^2 + 7, use the formula for the x-coordinate of the vertex: x = -b / (2a), where a = 4 and b = 0. Substitute these values into the formula to find x. Then, substitute the value of x back into the original equation to find the corresponding y-coordinate of the vertex. The axis of symmetry is the vertical line that passes through the vertex, given by the equation x = (x-coordinate of the vertex).