Solving Quadratic Equations by Graphing - Examples & Practice
Read this topicExplanations 3
- Solving quadratics by graphing is a great complement other approaches, like factoring. You can use it to verify that your solutions are correct. Regardless of the approach you t…
By Hannah Bonville, Alex Federspiel, Ruiran Xun, Jonathan Heller, Dani, Caroline K
- (Video) Solving Quadratic Equations by Graphing by Textbook Tactics This video by Textbook Tactics shows you how to solve a quadratic by graphing. Summary We normally see quadra…
By Jonathan Heller, Caroline K
- Solving Quadratic Equations by Graphing All quadratic equations have at most two solutions — these solutions can be real or imaginary. Some quadratic equations have two real sol…
By Caroline K
Problems 36
- Graph y=2x2+2y=2x^2+2y=2x2+2 and then find all solutions of 2x2+2=02x^2+2=02x2+2=0.
- The graph y=f(x)y = f(x)y=f(x) of a quadratic function is shown above, in blue. Find all points on the graph corresponding to the roots of f(x)f(x)f(x).
- The graph y=f(x)y = f(x)y=f(x) of a quadratic function is shown above, in green. Find all points on the graph corresponding to the zeros of f(x)f(x)f(x).
- The graph y=f(x)y = f(x)y=f(x) of a quadratic function is shown above. Which of the below points are not zeroes of the function?
- The graph y=f(x)y = f(x)y=f(x) of a quadratic function is shown above. Find all points on the graph corresponding to the roots of f(x)f(x)f(x).
- The graph y=f(x)y = f(x)y=f(x) of a quadratic function is shown above. Find all points on the graph corresponding to the roots of f(x)f(x)f(x).
- Solve the quadratic equation 3=−x2+73=-x^2+73=−x2+7 by graphing. Mark all solutions below.
- Find all real solutions xxx to the quadratic equation 3=x2+x−33=x^2+x-33=x2+x−3, by graphing.
- CONCEPT CHECK: The table above shows a quadratic function y(x)y(x)y(x). Where approximately are the roots?
- Suppose that the quadratic x2+bx+cx^2 + bx + cx2+bx+c has its vertex at (4,2)(4,2)(4,2). At most how many real roots can it have?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function with a>0a>0a>0 that has no solutions, what must be true of the vertex (x,y)(x,y)(x,y)?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function with a<0a<0a<0 that has no solutions, what must be true of the vertex (x,y)(x,y)(x,y)?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function with a>0a>0a>0 that has two real solutions, what must be true of the vertex (x,y)(x,y)(x,y)?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function with a<0a<0a<0 that has two real solutions, what must be true of the vertex (x,y)(x,y)(x,y)?
- Which of the parabolas graphed above is the graph of the function f(x)=−2x2−2x+2f(x)=-2x^2-2x+2f(x)=−2x2−2x+2?
- Which of the parabolas graphed above is the graph of the function f(x)=−x2+2x−2f(x)=-x^2+2x-2f(x)=−x2+2x−2?
- Which of the parabolas graphed above is the graph of the function f(x)=x2−x+1f(x)=x^2-x+1f(x)=x2−x+1?
- Which of the parabolas graphed above is the graph of the function f(x)=x2+xf(x)=x^2+xf(x)=x2+x?
- Graph the quadratic function f(x)=−2x2+2x+4f(x)=-2x^2+2x+4f(x)=−2x2+2x+4 and determine which two of the following points are zeros of the function.
- Graph the quadratic function f(x)=x2+4x−2f(x)=x^2+4x-2f(x)=x2+4x−2 and determine which two of the following points are zeros of the function.
- Graph the quadratic function f(x)=x2−3x−1f(x)=x^2-3x-1f(x)=x2−3x−1 and determine which two of the following points are zeros of the function.
- Concept check: plugging x=0x=0x=0 into a quadratic function will give you the \rule{1cm}{0.15mm} of the function.
- Find the minimum average speed at which R-Hood needs to be able to run to catch the ball before it lands. Round your answer to the nearest whole number.
- Where is/are the solution(s) of a set of quadratic equations on a graph?
- Where is/are the solution(s) to a single quadratic equation set equal to 000 on a graph?
- Identify the solution(s) when the individual equations of the parabolas are set equal to 000. Select all that apply.
- Identify the solution(s) for the individual parabolas when their quadratic equations are set equal to 000. Select all that apply.
- If the equations of these parabolas were set equal to 000, which parabola would have 000 solutions?
- If the equations of these parabolas were set equal to 000, which parabola would have 222 solutions?
- If the equations of these parabolas were set equal to 000, which parabola would have 111 solution?
- Where is/are the solution(s) of a linear-quadratic system on a graph?
- Identify the root(s) of the upward-opening quadratic graphed above.
- Which parabola above represents a quadratic function with a zero at x=0x=0x=0?
- Which parabola above represents a quadratic function that has both a positive root and a negative root?
- Identify the zero(s) of the downward-opening quadratic graphed above.
- The graph above y=f(x)y=f(x)y=f(x) is a quadratic function. Find all points on the graph corresponding to the zeros of f(x)f(x)f(x).