Graph y=4x^2+5x

Problem

y=4*x^2+5*x

Solution

1. Identify the type of function and its orientation. This is a quadratic function in the form y=a*x^2+b*x+c where a=4 b=5 and c=0 Since a>0 the parabola opens upward.

2. Find the x-intercepts by setting y=0 and factoring the expression.

0=x*(4*x+5)

x=0

4*x+5=0⇒x=−1.25

3. Find the y-intercept by evaluating the function at x=0

y=4*(0)^2+5*(0)=0

4. Calculate the vertex using the formula x=(−b)/(2*a)

x=(−5)/(2*(4))=−0.625

y=4*(−0.625)^2+5*(−0.625)=−1.5625

5. Determine the axis of symmetry, which is the vertical line passing through the vertex.

x=−0.625

6. Plot the points (0,0) (−1.25,0) and (−0.625,−1.5625) and draw a smooth U-shaped curve through them.

Final Answer

y=4*x^2+5*x

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