I need to find the vertex and make a graph using quadratics.
y=xsquared+11x+10
To find the vertex and graph the quadratic equation y = x^2 + 11x + 10, you can follow these steps:
Step 1: Identify the coefficients of the equation.
In the given equation, y = x^2 + 11x + 10, the coefficients are:
a = 1 (coefficient of x^2)
b = 11 (coefficient of x)
c = 10 (constant term)
Step 2: Find the x-coordinate of the vertex.
The x-coordinate of the vertex can be calculated using the formula: x = -b / (2*a).
Plug in the values from the equation: x = -11 / (2*1) = -11 / 2 = -5.5 (or -5.5 is the axis of symmetry).
Step 3: Find the y-coordinate of the vertex.
To find the y-coordinate of the vertex, substitute the x-coordinate (-5.5) back into the equation.
y = (-5.5)^2 + 11(-5.5) + 10
y = 30.25 - 60.5 + 10
y = -20.25
So, the vertex of the quadratic equation is (-5.5, -20.25).
Step 4: Plot the vertex on a graph.
Draw the x and y axes on a graph and plot the vertex (-5.5, -20.25) as a point.
Step 5: Determine the shape of the graph.
Since the coefficient of the x^2 term (a) is positive (1 in this case), the graph opens upwards, forming a U-shape.
Step 6: Find additional points.
To find more points for graphing, choose any x-value and substitute it into the equation to determine the corresponding y-value. For example, when x = -6, we can calculate y:
y = (-6)^2 + 11(-6) + 10
y = 36 - 66 + 10
y = -20
So, another point on the graph is (-6, -20).
Step 7: Plot additional points and complete the graph.
Use the calculated points to plot additional points on the graph. Connect the points smoothly to complete the graph of the quadratic equation y = x^2 + 11x + 10.