Sketching Quadratic Graphs
Read this topicExplanations 3
- (Video) Horizontal and Vertical Shifts by mathman1024 This video by mathman1024 shows how to sketch a graph given the vertex form. Summary\large{\text{Summary}}Summary The verte…
By Alex Federspiel, Vatsal Ojha, Amy Feraco, Jonathan Heller, Anusha Rahman
- Sketching Graphs of Quadratic Functions Let's make sure we know the definitions of some important terms. These will help us graph later. Parabola: graph of quadratic function in…
By Amy Feraco, Victor Wang, Jonathan Heller, Caroline K, Anusha Rahman
- Sketching Quadratic Graphs Take a look at aaa in a quadratic equation y=ax2+bx+c.y=ax^2+bx+c.y=ax2+bx+c. It can tell you a lot about the parabola!
By Caroline K
Problems 36
- 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?
- Do quadratic functions pass the horizontal line test?
- For which of the following quadratic graphs does the vertex represent a maximum value?
- Which of the following quadratic graphs open upward?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function, what must be true of aaa?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function that opens upwards, what must be true of aaa?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function that opens downwards, what must be true of aaa?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function with a<0a<0a<0, what is the xxx-value of the vertex?
- If f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c is a quadratic function with a<0a<0a<0, what is the yyy-value of the vertex?
- If the quadratic function f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c has a minimum value, what must be true of aaa?
- If the quadratic function f(x)=ax2+bx+cf(x)=ax^2+bx+cf(x)=ax2+bx+c has a maximum value, what must be true of aaa?
- 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?
- What is the axis of symmetry of the function f(x)=−2x2+4x−5f(x)=-2x^2+4x-5f(x)=−2x2+4x−5?
- What is the axis of symmetry of the function f(x)=−3x2−12x−8f(x)=-3x^2-12x-8f(x)=−3x2−12x−8?
- Suppose the coefficients a,b,ca,b,ca,b,c are integers with no common factor dividing all three coefficients. What is the value of bbb?
- Lydia is helping Cameron record his sales. She decides to factor the function for simpler calculations. \\ Write the function in factored form and determine if Cameron should st…
- Which equation is most likely to fit the scatter plot above?
- Which of the following graphs represents the function x2+3x+1x^{2}+3x+1x2+3x+1?
- Which of the graphs above represent the function f(x)=5x2+3x+2f(x)=5x^{2}+3x+2f(x)=5x2+3x+2?
- A quadratic function fff satisfies f(1)=f(2)=0f(1) = f(2) = 0f(1)=f(2)=0 and f(0)=2012f(0) = 2012f(0)=2012. What is f(−1)f(-1)f(−1)? Does the graph open upwards or downwards? So…
- Is it possible for two quadratic graphs which open upwards to intersect at exactly one point?
- Suppose two quadratic graphs share the same vertex. At how many points can these graphs intersect?
- Let f(x)f(x)f(x) and g(x)g(x)g(x) represent two distinct quadratic graphs. What is the maximum number of times f(x)f(x)f(x) and g(x)g(x)g(x) can intersect?
- The quadratic y=(x−4)2+8y = (x-4)^2+8y=(x−4)2+8 and the line y=cy = cy=c are tangent. What is the value of ccc? To be tangent means that they intersect at exactly one point.
- Which of the following graphs represents f(x)=−x2+2x−3f(x)= -x^2+2x-3f(x)=−x2+2x−3?
- Which of the following graphs represents the function f(x)=2x2+4xf(x) = 2x^2+4xf(x)=2x2+4x?
- f(x)f(x)f(x) is a quadratic equation with xxx intercepts at (3,0)(3,0)(3,0) and (5,0)(5,0)(5,0). Which of the following are possible yyy intercepts?
- Let f(x)=5x2+5x+2f(x) = 5x^2+5x+2f(x)=5x2+5x+2 and g(x)=8x2+8x+4g(x) = 8x^2+8x+4g(x)=8x2+8x+4. Suppose we found aaa such that ∣f(a)−g(a)∣|f(a) - g(a)|∣f(a)−g(a)∣ was as small as…
- The predicted amount of rain in Clovertown during the month of July is modeled by the function J(t)=0.02(t−13)2+0.05,J(t) = 0.02(t - 13)^2 + 0.05,J(t)=0.02(t−13)2+0.05, where tt…